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Number Theory Seminar
Seminar information archive ～05/21｜Next seminar｜Future seminars 05/22～
| Date, time & place | Wednesday 17:00 - 18:00 117Room #117 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | Naoki Imai, Shane Kelly |
Seminar information archive
2015/10/27
18:00-19:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Masanori Asakura (Hokkaido University)
On the period conjecture of Gross-Deligne for fibrations (English)
Masanori Asakura (Hokkaido University)
On the period conjecture of Gross-Deligne for fibrations (English)
[ Abstract ]
The period conjecture of Gross-Deligne asserts that the periods of algebraic varieties with complex multiplication are products of values of the gamma function at rational numbers. This is proved for CM elliptic curves by Lerch-Chowla-Selberg, and for abelian varieties by Shimura-Deligne-Anderson. However the question in the general case is still open. In this talk, we verify an alternating variant of the period conjecture for the cohomology of fibrations with relative multiplication. The proof relies on the Saito-Terasoma product formula for epsilon factors of integrable regular singular connections and the Riemann-Roch-Hirzebruch theorem. This is a joint work with Javier Fresan.
The period conjecture of Gross-Deligne asserts that the periods of algebraic varieties with complex multiplication are products of values of the gamma function at rational numbers. This is proved for CM elliptic curves by Lerch-Chowla-Selberg, and for abelian varieties by Shimura-Deligne-Anderson. However the question in the general case is still open. In this talk, we verify an alternating variant of the period conjecture for the cohomology of fibrations with relative multiplication. The proof relies on the Saito-Terasoma product formula for epsilon factors of integrable regular singular connections and the Riemann-Roch-Hirzebruch theorem. This is a joint work with Javier Fresan.
2015/09/30
17:00-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Alan Lauder (University of Oxford)
Stark points and p-adic iterated integrals attached to modular forms of weight one (English)
Alan Lauder (University of Oxford)
Stark points and p-adic iterated integrals attached to modular forms of weight one (English)
[ Abstract ]
Given an elliptic curve over Q the only well-understood construction of global points is that of "Heegner points", which are defined over ring class fields of imaginary quadratic fields and are non-torsion only in rank one settings. I will present some new constructions and explicit formulae, in situations of rank one and two, of global points over ring class fields of real or imaginary quadratic fields, cyclotomic fields, and extensions of Q with Galois group A_4, S_4 or A_5. Our constructions and formulae are proven in certain cases - when they can be related to Heegner points - and conjectural, but supported by experimental evidence, otherwise. This is joint work with Henri Darmon and Victor Rotger.
Given an elliptic curve over Q the only well-understood construction of global points is that of "Heegner points", which are defined over ring class fields of imaginary quadratic fields and are non-torsion only in rank one settings. I will present some new constructions and explicit formulae, in situations of rank one and two, of global points over ring class fields of real or imaginary quadratic fields, cyclotomic fields, and extensions of Q with Galois group A_4, S_4 or A_5. Our constructions and formulae are proven in certain cases - when they can be related to Heegner points - and conjectural, but supported by experimental evidence, otherwise. This is joint work with Henri Darmon and Victor Rotger.
2015/09/09
17:00-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Emmanuel Ullmo (IHES)
The hyperbolic Ax-Lindemann conjecture (English)
Emmanuel Ullmo (IHES)
The hyperbolic Ax-Lindemann conjecture (English)
[ Abstract ]
The hyperbolic Ax Lindemann conjecture is a functional transcendental statement which describes the Zariski closure of "algebraic flows" on Shimura varieties. We will describe the proof of this conjecture and its consequences for the André-Oort conjecture. This is a joint work with Bruno Klingler and Andrei Yafaev.
The hyperbolic Ax Lindemann conjecture is a functional transcendental statement which describes the Zariski closure of "algebraic flows" on Shimura varieties. We will describe the proof of this conjecture and its consequences for the André-Oort conjecture. This is a joint work with Bruno Klingler and Andrei Yafaev.
2015/07/23
13:00-16:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Lasse Grimmelt (University of Göttingen/Waseda University) 13:00-14:00
Representation of squares by cubic forms - Estimates for the appearing exponential sums (English)
Haoyu Hu (University of Tokyo) 14:15-15:15
Ramification and nearby cycles for $\ell$-adic sheaves on relative curves (English)
Explicit computation of the number of dormant opers and duality (Japanese)
Lasse Grimmelt (University of Göttingen/Waseda University) 13:00-14:00
Representation of squares by cubic forms - Estimates for the appearing exponential sums (English)
Haoyu Hu (University of Tokyo) 14:15-15:15
Ramification and nearby cycles for $\ell$-adic sheaves on relative curves (English)
[ Abstract ]
I will present a new approach for a formula of Deligne and Kato that computes the dimension of the nearby cycle complex of an $\ell$-adic sheaf on a smooth relative curve over a strictly henselian trait such that $p$ is not one of its uniformizer. Deligne considered the case where the sheaf has no vertical ramification and Kato extended the formula to the general case. My approach is based on ramification theory of Abbes and Saito. It computes the nearby cycle complex in terms of the refined Swan conductor. In fact, I compare Abbes-Saito's refined Swan conductor with Kato's Swan conductor with differential values, which is the key ingredient in Kato's formula; the case of rank one sheaves is due to Abbes and Saito. My approach provides also a new independent proof of Deligne-Kato's formula.
Yasuhiro Wakabayashi (University of Tokyo) 15:30-16:30I will present a new approach for a formula of Deligne and Kato that computes the dimension of the nearby cycle complex of an $\ell$-adic sheaf on a smooth relative curve over a strictly henselian trait such that $p$ is not one of its uniformizer. Deligne considered the case where the sheaf has no vertical ramification and Kato extended the formula to the general case. My approach is based on ramification theory of Abbes and Saito. It computes the nearby cycle complex in terms of the refined Swan conductor. In fact, I compare Abbes-Saito's refined Swan conductor with Kato's Swan conductor with differential values, which is the key ingredient in Kato's formula; the case of rank one sheaves is due to Abbes and Saito. My approach provides also a new independent proof of Deligne-Kato's formula.
Explicit computation of the number of dormant opers and duality (Japanese)
2015/06/17
17:00-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Norifumi Seki (University of Tokyo)
Hodge-Tate weights of p-adic Galois representations and Banach representations of GL_2(Q_p)
(Japanese)
Norifumi Seki (University of Tokyo)
Hodge-Tate weights of p-adic Galois representations and Banach representations of GL_2(Q_p)
(Japanese)
2015/05/27
17:00-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Ippei Nagamachi (University of Tokyo)
On a good reduction criterion for polycurves with sections (Japanese)
Ippei Nagamachi (University of Tokyo)
On a good reduction criterion for polycurves with sections (Japanese)
2015/05/20
17:30-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Shou-Wu Zhang (Princeton University)
Colmez' conjecture in average (English)
Shou-Wu Zhang (Princeton University)
Colmez' conjecture in average (English)
[ Abstract ]
This is a report on a joint work with Xinyi Yuan on a conjectured formula of Colmez about the Faltings heights of CM abelian varieties. I will sketch a deduction of this formula in average of CM types from our early work on Gross-Zagier formula. When combined with a recent work of Tsimerman, this result implies the Andre-Oort conjecture for the moduli of abelian varieties.
Our method is different than a recently announced proof of a weaker form of the average formula by Andreatta, Howard, Goren, and Madapusi Pera: we use neither high dimensional Shimura varieties nor Borcherds' liftings.
This is a report on a joint work with Xinyi Yuan on a conjectured formula of Colmez about the Faltings heights of CM abelian varieties. I will sketch a deduction of this formula in average of CM types from our early work on Gross-Zagier formula. When combined with a recent work of Tsimerman, this result implies the Andre-Oort conjecture for the moduli of abelian varieties.
Our method is different than a recently announced proof of a weaker form of the average formula by Andreatta, Howard, Goren, and Madapusi Pera: we use neither high dimensional Shimura varieties nor Borcherds' liftings.
2015/04/08
17:30-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Seidai Yasuda (Osaka University)
Integrality of $p$-adic multiple zeta values and application to finite multiple zeta values.
(English)
Seidai Yasuda (Osaka University)
Integrality of $p$-adic multiple zeta values and application to finite multiple zeta values.
(English)
[ Abstract ]
I will give a proof of an integrality of p-adic multiple zeta values. I would also like to explain how it can be applied to give an upper bound of the dimension of finite multiple zeta values.
I will give a proof of an integrality of p-adic multiple zeta values. I would also like to explain how it can be applied to give an upper bound of the dimension of finite multiple zeta values.
2015/02/18
16:40-17:40 Room #056 (Graduate School of Math. Sci. Bldg.)
Piotr Achinger (University of California, Berkeley)
Wild ramification and $K(\pi, 1)$ spaces (English)
Piotr Achinger (University of California, Berkeley)
Wild ramification and $K(\pi, 1)$ spaces (English)
[ Abstract ]
A smooth variety in characteristic zero is Zariski-locally a $K(\pi,1)$ space, i.e., has trivial higher homotopy groups. This fact is of crucial importance in Artin's proof that $\ell$-adic cohomology agrees with singular cohomology over $\mathbb{C}$. The characteristic $p$ variant of this is not known --- we do not even know whether the affine plane is a $K(\pi, 1)$ in positive characteristic! I will show how to reduce this question to a ``Bertini-type’' statement regarding wild ramification of $\ell$-adic local systems on affine spaces, which might be of independent interest. I will verify this statement in the special case of local systems of rank $1$ and speculate on how one might treat the general case.
A smooth variety in characteristic zero is Zariski-locally a $K(\pi,1)$ space, i.e., has trivial higher homotopy groups. This fact is of crucial importance in Artin's proof that $\ell$-adic cohomology agrees with singular cohomology over $\mathbb{C}$. The characteristic $p$ variant of this is not known --- we do not even know whether the affine plane is a $K(\pi, 1)$ in positive characteristic! I will show how to reduce this question to a ``Bertini-type’' statement regarding wild ramification of $\ell$-adic local systems on affine spaces, which might be of independent interest. I will verify this statement in the special case of local systems of rank $1$ and speculate on how one might treat the general case.
2015/01/21
18:00-19:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Ofer Gabber (CNRS, IHES)
Spreading-out of rigid-analytic families and observations on p-adic Hodge theory (English)
Ofer Gabber (CNRS, IHES)
Spreading-out of rigid-analytic families and observations on p-adic Hodge theory (English)
[ Abstract ]
(Joint work with Brian Conrad.) Let $K$ be a complete rank 1 valued field with ring of integers $O_K$, $A$ an adic noetherian ring and $f:A\to O_K$ an adic morphism. If $g:X\to Y$ is a proper flat morphism between rigid analytic spaces over $K$ then locally on $Y$ a flat formal model of $g$ spreads out to a proper flat morphism between formal schemes topologically of finite type over $A$. As an application one can prove that for proper smooth $g$ and $K$ of characteristic 0, the Hodge to de Rham spectral sequence for $g$ degenerates and the $R^q g_* \Omega^p_{X/Y}$ are locally free.
(Joint work with Brian Conrad.) Let $K$ be a complete rank 1 valued field with ring of integers $O_K$, $A$ an adic noetherian ring and $f:A\to O_K$ an adic morphism. If $g:X\to Y$ is a proper flat morphism between rigid analytic spaces over $K$ then locally on $Y$ a flat formal model of $g$ spreads out to a proper flat morphism between formal schemes topologically of finite type over $A$. As an application one can prove that for proper smooth $g$ and $K$ of characteristic 0, the Hodge to de Rham spectral sequence for $g$ degenerates and the $R^q g_* \Omega^p_{X/Y}$ are locally free.
2015/01/14
16:40-17:40 Room #056 (Graduate School of Math. Sci. Bldg.)
Laurent Berger (ENS de Lyon)
Iterate extensions and relative Lubin-Tate groups
Laurent Berger (ENS de Lyon)
Iterate extensions and relative Lubin-Tate groups
[ Abstract ]
Let K be a p-adic field, let P(T) be a polynomial with coefficients in K, and let {$u_n$} be a sequence such that $P(u_{n+1}) = u_n$ for all n and $u_0$ belongs to K. The extension of K generated by the $u_n$ is called an iterate extension. I will discuss these extensions, show that under certain favorable conditions there is a theory of Coleman power series, and explain the relationship with relative Lubin-Tate groups.
Let K be a p-adic field, let P(T) be a polynomial with coefficients in K, and let {$u_n$} be a sequence such that $P(u_{n+1}) = u_n$ for all n and $u_0$ belongs to K. The extension of K generated by the $u_n$ is called an iterate extension. I will discuss these extensions, show that under certain favorable conditions there is a theory of Coleman power series, and explain the relationship with relative Lubin-Tate groups.
2015/01/07
16:40-17:40 Room #056 (Graduate School of Math. Sci. Bldg.)
Sandra Rozensztajn (ENS de Lyon)
Congruences of modular forms modulo p and a variant of the Breuil-Mézard conjecture (English)
Sandra Rozensztajn (ENS de Lyon)
Congruences of modular forms modulo p and a variant of the Breuil-Mézard conjecture (English)
[ Abstract ]
In this talk I will explain how a problem of congruences modulo p in the space of modular forms $S_k(\Gamma_0(p))$ is related to the geometry of some deformation spaces of Galois representations and can be solved by using a variant of the Breuil-Mézard conjecture.
In this talk I will explain how a problem of congruences modulo p in the space of modular forms $S_k(\Gamma_0(p))$ is related to the geometry of some deformation spaces of Galois representations and can be solved by using a variant of the Breuil-Mézard conjecture.
2014/12/17
18:00-19:00 Room #117 (Graduate School of Math. Sci. Bldg.)
Konstantin Ardakov (University of Oxford)
Equivariant $\wideparen{\mathcal{D}}$ modules on rigid analytic spaces
(English)
Konstantin Ardakov (University of Oxford)
Equivariant $\wideparen{\mathcal{D}}$ modules on rigid analytic spaces
(English)
[ Abstract ]
Locally analytic representations of p-adic Lie groups are of interest in several branches of arithmetic algebraic geometry, notably the p-adic local Langlands program. I will discuss some work in progress towards a Beilinson-Bernstein style localisation theorem for admissible locally analytic representations of semisimple compact p-adic Lie groups using equivariant formal models of rigid analytic flag varieties.
Locally analytic representations of p-adic Lie groups are of interest in several branches of arithmetic algebraic geometry, notably the p-adic local Langlands program. I will discuss some work in progress towards a Beilinson-Bernstein style localisation theorem for admissible locally analytic representations of semisimple compact p-adic Lie groups using equivariant formal models of rigid analytic flag varieties.
2014/11/19
16:40-17:40 Room #056 (Graduate School of Math. Sci. Bldg.)
Fabien Pazuki (Univ Bordeaux and Univ Copenhagen)
Bad reduction of curves with CM jacobians (English)
Fabien Pazuki (Univ Bordeaux and Univ Copenhagen)
Bad reduction of curves with CM jacobians (English)
[ Abstract ]
An abelian variety defined over a number field and having complex multiplication (CM) has potentially good reduction everywhere. If a curve of positive genus which is defined over a number field has good reduction at a given finite place, then so does its jacobian variety. However, the converse statement is false already in the genus 2 case, as can be seen in the entry $[I_0-I_0-m]$ in Namikawa and Ueno's classification table of fibres in pencils of curves of genus 2. In this joint work with Philipp Habegger, our main result states that this phenomenon prevails for certain families of curves.
We prove the following result: Let F be a real quadratic number field. Up to isomorphisms there are only finitely many curves C of genus 2 defined over $\overline{\mathbb{Q}}$ with good reduction everywhere and such that the jacobian Jac(C) has CM by the maximal order of a quartic, cyclic, totally imaginary number field containing F. Hence such a curve will almost always have stable bad reduction at some prime whereas its jacobian has good reduction everywhere. A remark is that one can exhibit an infinite family of genus 2 curves with CM jacobian such that the endomorphism ring is the ring of algebraic integers in a cyclic extension of $\mathbb{Q}$ of degree 4 that contains $\mathbb{Q}(\sqrt{5})$, for example.
An abelian variety defined over a number field and having complex multiplication (CM) has potentially good reduction everywhere. If a curve of positive genus which is defined over a number field has good reduction at a given finite place, then so does its jacobian variety. However, the converse statement is false already in the genus 2 case, as can be seen in the entry $[I_0-I_0-m]$ in Namikawa and Ueno's classification table of fibres in pencils of curves of genus 2. In this joint work with Philipp Habegger, our main result states that this phenomenon prevails for certain families of curves.
We prove the following result: Let F be a real quadratic number field. Up to isomorphisms there are only finitely many curves C of genus 2 defined over $\overline{\mathbb{Q}}$ with good reduction everywhere and such that the jacobian Jac(C) has CM by the maximal order of a quartic, cyclic, totally imaginary number field containing F. Hence such a curve will almost always have stable bad reduction at some prime whereas its jacobian has good reduction everywhere. A remark is that one can exhibit an infinite family of genus 2 curves with CM jacobian such that the endomorphism ring is the ring of algebraic integers in a cyclic extension of $\mathbb{Q}$ of degree 4 that contains $\mathbb{Q}(\sqrt{5})$, for example.
2014/11/12
18:00-19:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Ruochuan Liu (BICMR)
Relative (φ, Γ)-modules (English)
Ruochuan Liu (BICMR)
Relative (φ, Γ)-modules (English)
[ Abstract ]
In this talk, we will introduce the theory of (φ, Γ)-modules for general adic spaces. This is a joint work with Kedlaya.
In this talk, we will introduce the theory of (φ, Γ)-modules for general adic spaces. This is a joint work with Kedlaya.
2014/10/28
16:40-18:50 Room #002 (Graduate School of Math. Sci. Bldg.)
Judith Ludwig (Imperial college) 16:40-17:40
A p-adic Labesse-Langlands transfer (English)
Plectic cohomology (English)
Judith Ludwig (Imperial college) 16:40-17:40
A p-adic Labesse-Langlands transfer (English)
[ Abstract ]
Let B be a definite quaternion algebra over the rationals, G the algebraic group defined by the units in B and H the subgroup of G of norm one elements. Then the classical transfer of automorphic representations from G to H is well understood thanks to Labesse and Langlands, who proved formulas for the multiplicity of irreducible admissible representations of H(adeles) in the discrete automorphic spectrum.
The goal of this talk is to prove a p-adic version of this transfer. By this we mean an extension of the classical transfer to p-adic families of automorphic forms as parametrized by certain rigid analytic spaces called eigenvarieties. We will prove the p-adic transfer by constructing a morphism between eigenvarieties, which agrees with the classical transfer on points corresponding to classical automorphic representations.
Jan Nekovar (Université Paris 6) 17:50-18:50Let B be a definite quaternion algebra over the rationals, G the algebraic group defined by the units in B and H the subgroup of G of norm one elements. Then the classical transfer of automorphic representations from G to H is well understood thanks to Labesse and Langlands, who proved formulas for the multiplicity of irreducible admissible representations of H(adeles) in the discrete automorphic spectrum.
The goal of this talk is to prove a p-adic version of this transfer. By this we mean an extension of the classical transfer to p-adic families of automorphic forms as parametrized by certain rigid analytic spaces called eigenvarieties. We will prove the p-adic transfer by constructing a morphism between eigenvarieties, which agrees with the classical transfer on points corresponding to classical automorphic representations.
Plectic cohomology (English)
2014/10/14
17:30-18:30 Room #002 (Graduate School of Math. Sci. Bldg.)
Fabrizio Andreatta (Università Statale di Milano)
A p-adic criterion for good reduction of curves (ENGLISH)
Fabrizio Andreatta (Università Statale di Milano)
A p-adic criterion for good reduction of curves (ENGLISH)
[ Abstract ]
Given a curve over a dvr of mixed characteristic 0-p with smooth generic fiber and with semistable reduction, I will present a criterion for good reduction in terms of the (unipotent) p-adic étale fundamental group of its generic fiber.
Given a curve over a dvr of mixed characteristic 0-p with smooth generic fiber and with semistable reduction, I will present a criterion for good reduction in terms of the (unipotent) p-adic étale fundamental group of its generic fiber.
2014/06/25
16:40-17:40 Room #056 (Graduate School of Math. Sci. Bldg.)
Masahiko Takiguchi (University of Tokyo)
Periods of some two dimensional reducible p-adic representations and non-de Rham B-pairs (JAPANESE)
Masahiko Takiguchi (University of Tokyo)
Periods of some two dimensional reducible p-adic representations and non-de Rham B-pairs (JAPANESE)
2014/06/17
17:30-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Bao Châu Ngô (University of Chicago, VIASM)
Vinberg's monoid and automorphic L-functions (ENGLISH)
Bao Châu Ngô (University of Chicago, VIASM)
Vinberg's monoid and automorphic L-functions (ENGLISH)
[ Abstract ]
We will explain a generalisation of the construction of the local factors of Godement-Jacquet's L-functions, based on Vinberg's monoid.
We will explain a generalisation of the construction of the local factors of Godement-Jacquet's L-functions, based on Vinberg's monoid.
2014/05/28
16:40-17:40 Room #056 (Graduate School of Math. Sci. Bldg.)
Gantsooj Batzaya (University of Tokyo)
On simultaneous approximation to powers of a real number by rational numbers (ENGLISH)
Gantsooj Batzaya (University of Tokyo)
On simultaneous approximation to powers of a real number by rational numbers (ENGLISH)
2014/05/21
17:30-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Shenghao Sun (Mathematical Sciences Center of Tsinghua University)
Parity of Betti numbers in étale cohomology (ENGLISH)
Shenghao Sun (Mathematical Sciences Center of Tsinghua University)
Parity of Betti numbers in étale cohomology (ENGLISH)
[ Abstract ]
By Hodge symmetry, the Betti numbers of a complex projective smooth variety in odd degrees are even. When the base field has characteristic p, Deligne proved the hard Lefschetz theorem in etale cohomology, and the parity result follows from this. Suh has generalized this to proper smooth varieties in characteristic p, using crystalline cohomology.
The purity of intersection cohomology group of proper varieties suggests that the same parity property should hold for these groups in characteristic p. We proved this by investigating the symmetry in the categorical level.
In particular, we reproved Suh's result, using merely etale cohomology. Some related results will be discussed. This is joint work with Weizhe Zheng.
By Hodge symmetry, the Betti numbers of a complex projective smooth variety in odd degrees are even. When the base field has characteristic p, Deligne proved the hard Lefschetz theorem in etale cohomology, and the parity result follows from this. Suh has generalized this to proper smooth varieties in characteristic p, using crystalline cohomology.
The purity of intersection cohomology group of proper varieties suggests that the same parity property should hold for these groups in characteristic p. We proved this by investigating the symmetry in the categorical level.
In particular, we reproved Suh's result, using merely etale cohomology. Some related results will be discussed. This is joint work with Weizhe Zheng.
2014/04/30
16:40-17:40 Room #056 (Graduate School of Math. Sci. Bldg.)
Takuya Maruyama (University of Tokyo)
An effective upper bound for the number of principally polarized Abelian schemes (JAPANESE)
Takuya Maruyama (University of Tokyo)
An effective upper bound for the number of principally polarized Abelian schemes (JAPANESE)
2014/04/23
16:40-17:40 Room #002 (Graduate School of Math. Sci. Bldg.)
Yoichi Mieda (University of Tokyo)
Non-tempered A-packets and the Rapoport-Zink spaces (JAPANESE)
Yoichi Mieda (University of Tokyo)
Non-tempered A-packets and the Rapoport-Zink spaces (JAPANESE)
2014/04/16
17:30-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Olivier Wittenberg (ENS and CNRS)
On the cycle class map for zero-cycles over local fields (ENGLISH)
Olivier Wittenberg (ENS and CNRS)
On the cycle class map for zero-cycles over local fields (ENGLISH)
[ Abstract ]
The Chow group of zero-cycles of a smooth and projective variety defined over a field k is an invariant of an arithmetic and geometric nature which is well understood only when k is a finite field (by higher-dimensional class field theory). In this talk, we will discuss the case of local and strictly local fields. We prove in particular the injectivity of the cycle class map to integral l-adic cohomology for a large class of surfaces with positive geometric genus over p-adic fields. The same statement holds for semistable K3 surfaces over C((t)), but does not hold in general for surfaces over C((t)) or over the maximal unramified extension of a p-adic field. This is a joint work with Hélène Esnault.
The Chow group of zero-cycles of a smooth and projective variety defined over a field k is an invariant of an arithmetic and geometric nature which is well understood only when k is a finite field (by higher-dimensional class field theory). In this talk, we will discuss the case of local and strictly local fields. We prove in particular the injectivity of the cycle class map to integral l-adic cohomology for a large class of surfaces with positive geometric genus over p-adic fields. The same statement holds for semistable K3 surfaces over C((t)), but does not hold in general for surfaces over C((t)) or over the maximal unramified extension of a p-adic field. This is a joint work with Hélène Esnault.
2014/02/05
17:10-18:10 Room #002 (Graduate School of Math. Sci. Bldg.)
Neven Grbac (University of Rijeka)
The Franke filtration of spaces of automorphic forms (ENGLISH)
Neven Grbac (University of Rijeka)
The Franke filtration of spaces of automorphic forms (ENGLISH)
[ Abstract ]
The Franke filtration is a filtration of the space of all adelic automorphic forms on a reductive group defined over a number field. The filtration steps can be described as certain induced representations, which has applications to the study of Eisenstein cohomology. In this talk, we shall describe the Franke filtration in general, give several examples, and explain its connection to cohomology.
The Franke filtration is a filtration of the space of all adelic automorphic forms on a reductive group defined over a number field. The filtration steps can be described as certain induced representations, which has applications to the study of Eisenstein cohomology. In this talk, we shall describe the Franke filtration in general, give several examples, and explain its connection to cohomology.
