代数学コロキウム

過去の記録 ~09/27次回の予定今後の予定 09/28~

開催情報 水曜日 17:00~18:00 数理科学研究科棟(駒場) 056号室
担当者 今井 直毅, 三枝 洋一

過去の記録

2016年04月20日(水)

17:00-18:00   数理科学研究科棟(駒場) 056号室
戸次鵬人 氏 (東京大学数理科学研究科)
On periodicity of geodesic continued fractions (Japanese)

2016年04月13日(水)

17:30-18:30   数理科学研究科棟(駒場) 056号室
玉川安騎男 氏 (京都大学数理解析研究所)
Semisimplicity of geometric monodromy on etale cohomology (joint work with Anna Cadoret and Chun Yin Hui)

(English)
[ 講演概要 ]
Let K be a function field over an algebraically closed field of characteritic p \geq 0, X a proper smooth K-scheme, and l a prime distinct from p. Deligne proved that the Q_l-coefficient etale cohomology groups of the geometric fiber of X --> K are always semisimple as G_K-modules. In this talk, we consider a similar problem for the F_l-coefficient etale cohomology groups. Among other things, we show that if p=0 (resp. in general), they are semisimple for all but finitely many l's (resp. for all l's in a set of density 1).

(本講演は「東京北京パリ数論幾何セミナー」として, インターネットによる東大数理, Morningside Center of MathematicsとIHESの双方向同時中継で行います.)

2016年03月29日(火)

17:30-18:30   数理科学研究科棟(駒場) 002号室
曜日・部屋がいつもと異なりますのでご注意ください.
Matthew Morrow 氏 (Universität Bonn)
Motivic cohomology of formal schemes in characteristic p
(English)
[ 講演概要 ]
The logarithmic Hodge-Witt sheaves of Illusie, Milne, Kato, et al. of a smooth variety in characteristic p provide a concrete realisation of its p-adic motivic cohomology, thanks to results of Geisser-Levine and Bloch-Kato-Gabber which link them to algebraic K-theory. I will explain an analogous theory for formal schemes, as well as applications to algebraic cycles, such as a weak Lefschetz theorem for formal Chow groups.

(本講演は「東京北京パリ数論幾何セミナー」として, インターネットによる東大数理, Morningside Center of MathematicsとIHESの双方向同時中継で行います.)

2015年12月09日(水)

18:00-19:00   数理科学研究科棟(駒場) 056号室
Ted Chinburg 氏 (University of Pennsylvania & IHES)
Chern classes in Iwasawa theory (English)
[ 講演概要 ]
Many of the main conjectures in Iwasawa theory can be phrased as saying that the first Chern class of an Iwasawa module is generated by a p-adic L-series. In this talk I will describe how higher Chern classes pertain to the higher codimension behavior of Iwasawa modules. I'll then describe a template for conjectures which would link such higher Chern classes to elements in the K-theory of Iwasawa algebras which are constructed from tuples of Katz p-adic L-series. I will finally describe an instance in which a result of this kind, for the second Chern class of an unramified Iwasawa module, can be proved over an imaginary quadratic field. This is joint work with F. Bleher, R. Greenberg, M. Kakde, G. Pappas, R. Sharifi and M. J. Taylor.

(本講演は「東京北京パリ数論幾何セミナー」として, インターネットによる東大数理, Morningside Center of MathematicsとIHESの双方向同時中継で行います.)

2015年11月17日(火)

18:00-19:00   数理科学研究科棟(駒場) 117号室
いつもと曜日が異なりますのでご注意ください
Dennis Gaitsgory 氏 (Harvard University & IHES)
The Tamagawa number formula over function fields. (English)
[ 講演概要 ]
Let G be a semi-simple and simply connected group and X an algebraic curve. We consider $Bun_G(X)$, the moduli space of G-bundles on X. In their celebrated paper, Atiyah and Bott gave a formula for the cohomology of $Bun_G$, namely $H^*(Bun_G)=Sym(H_*(X)\otimes V)$, where V is the space of generators for $H^*_G(pt)$. When we take our ground field to be a finite field, the Atiyah-Bott formula implies the Tamagawa number conjecture for the function field of X.

The caveat here is that the A-B proof uses the interpretation of $Bun_G$ as the space of connection forms modulo gauge transformations, and thus only works over complex numbers (but can be extend to any field of characteristic zero). In the talk we will outline an algebro-geometric proof that works over any ground field. As its main geometric ingredient, it uses the fact that the space of rational maps from X to G is homologically contractible. Because of the nature of the latter statement, the proof necessarily uses tools from higher category theory. So, it can be regarded as an example how the latter can be used to prove something concrete: a construction at the level of 2-categories leads to an equality of numbers.

(本講演は「東京北京パリ数論幾何セミナー」として, インターネットによる東大数理, Morningside Center of MathematicsとIHESの双方向同時中継で行います.)

2015年10月27日(火)

18:00-19:00   数理科学研究科棟(駒場) 002号室
曜日・部屋がいつもと異なりますのでご注意ください
朝倉政典 氏 (北海道大学)
On the period conjecture of Gross-Deligne for fibrations (English)
[ 講演概要 ]
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.

(本講演は「東京北京パリ数論幾何セミナー」として, インターネットによる東大数理, Morningside Center of MathematicsとIHESの双方向同時中継で行います.)

2015年09月30日(水)

17:00-18:00   数理科学研究科棟(駒場) 056号室
Alan Lauder 氏 (University of Oxford)
Stark points and p-adic iterated integrals attached to modular forms of weight one (English)
[ 講演概要 ]
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年09月09日(水)

17:00-18:00   数理科学研究科棟(駒場) 056号室
Emmanuel Ullmo 氏 (IHES)
The hyperbolic Ax-Lindemann conjecture (English)
[ 講演概要 ]
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年07月23日(木)

13:00-16:30   数理科学研究科棟(駒場) 056号室
Lasse Grimmelt 氏 (ゲッティンゲン大学/早稲田大学) 13:00-14:00
Representation of squares by cubic forms - Estimates for the appearing exponential sums (English)
Haoyu Hu 氏 (東京大学数理科学研究科) 14:15-15:15
Ramification and nearby cycles for $\ell$-adic sheaves on relative curves (English)
[ 講演概要 ]
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.
若林 泰央 氏 (東京大学数理科学研究科) 15:30-16:30
Explicit computation of the number of dormant opers and duality (Japanese)

2015年06月17日(水)

17:00-18:00   数理科学研究科棟(駒場) 056号室
関 典史 氏 (東京大学数理科学研究科)
Hodge-Tate weights of p-adic Galois representations and Banach representations of GL_2(Q_p)
(Japanese)
[ 講演概要 ]
p進Galois表現のHodge-Tate重みを,p進Langlands対応により対応するGL_2(Q_p)のBanach表現から取り出すことが目標です.Banach表現の局所解析的ベクトルのなす空間へのLie環の作用からHodge-Tate重みが取り出せるというのが主結果で,Hodge-Tate表現の場合の局所代数的ベクトルについてのColmezの結果の解析的類似になっています.

2015年05月27日(水)

17:00-18:00   数理科学研究科棟(駒場) 056号室
長町一平 氏 (東京大学数理科学研究科)
On a good reduction criterion for polycurves with sections (Japanese)

2015年05月20日(水)

17:30-18:30   数理科学研究科棟(駒場) 056号室
Shou-Wu Zhang 氏 (Princeton University)
Colmez' conjecture in average (English)
[ 講演概要 ]
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.
(本講演は「東京北京パリ数論幾何セミナー」として, インターネットによる東大数理, Morningside Center of MathematicsとIHESの双方向同時中継で行います.)

2015年04月08日(水)

17:30-18:30   数理科学研究科棟(駒場) 056号室
安田正大 氏 (大阪大学)
Integrality of $p$-adic multiple zeta values and application to finite multiple zeta values.
(English)
[ 講演概要 ]
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.
(本講演は「東京北京パリ数論幾何セミナー」として, インターネットによる東大数理, Morningside Center of MathematicsとIHESの双方向同時中継で行います.)

2015年02月18日(水)

16:40-17:40   数理科学研究科棟(駒場) 056号室
Piotr Achinger 氏 (University of California, Berkeley)
Wild ramification and $K(\pi, 1)$ spaces (English)
[ 講演概要 ]
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年01月21日(水)

18:00-19:00   数理科学研究科棟(駒場) 056号室
Ofer Gabber 氏 (CNRS, IHES)
Spreading-out of rigid-analytic families and observations on p-adic Hodge theory (English)
[ 講演概要 ]
(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.
(本講演は「東京北京パリ数論幾何セミナー」として, インターネットによる東大数理, Morningside Center of MathematicsとIHESの双方向同時中継で行います.)

2015年01月14日(水)

16:40-17:40   数理科学研究科棟(駒場) 056号室
Laurent Berger 氏 (ENS de Lyon)
Iterate extensions and relative Lubin-Tate groups
[ 講演概要 ]
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年01月07日(水)

16:40-17:40   数理科学研究科棟(駒場) 056号室
Sandra Rozensztajn 氏 (ENS de Lyon)
Congruences of modular forms modulo p and a variant of the Breuil-Mézard conjecture (English)
[ 講演概要 ]
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年12月17日(水)

18:00-19:00   数理科学研究科棟(駒場) 117号室
いつもと教室が異なりますのでご注意ください
Konstantin Ardakov 氏 (University of Oxford)
Equivariant $\wideparen{\mathcal{D}}$ modules on rigid analytic spaces
(English)
[ 講演概要 ]
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.
(本講演は「東京北京パリ数論幾何セミナー」として, インターネットによる東大数理, Morningside Center of MathematicsとIHESの双方向同時中継で行います.)

2014年11月19日(水)

16:40-17:40   数理科学研究科棟(駒場) 056号室
Fabien Pazuki 氏 (Univ Bordeaux and Univ Copenhagen)
Bad reduction of curves with CM jacobians (English)
[ 講演概要 ]
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年11月12日(水)

18:00-19:00   数理科学研究科棟(駒場) 056号室
Ruochuan Liu 氏 (BICMR)
Relative (φ, Γ)-modules (English)
[ 講演概要 ]
In this talk, we will introduce the theory of (φ, Γ)-modules for general adic spaces. This is a joint work with Kedlaya.
(本講演は「東京北京パリ数論幾何セミナー」として, インターネットによる東大数理, Morningside Center of MathematicsとIHESの双方向同時中継で行います.)

2014年10月28日(火)

16:40-18:50   数理科学研究科棟(駒場) 002号室
いつもと曜日が異なりますのでご注意下さい
Judith Ludwig 氏 (Imperial college) 16:40-17:40
A p-adic Labesse-Langlands transfer (English)
[ 講演概要 ]
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 氏 (Université Paris 6) 17:50-18:50
Plectic cohomology (English)

2014年10月14日(火)

17:30-18:30   数理科学研究科棟(駒場) 002号室
いつもと曜日が違いますのでご注意ください.
Fabrizio Andreatta 氏 (Università Statale di Milano)
A p-adic criterion for good reduction of curves (ENGLISH)
[ 講演概要 ]
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.

(本講演は「東京北京パリ数論幾何セミナー」として, インターネットによる東大数理, Morningside Center of MathematicsとIHESの双方向同時中継で行います.)

2014年06月25日(水)

16:40-17:40   数理科学研究科棟(駒場) 056号室
滝口 正彦 氏 (東京大学数理科学研究科)
Periods of some two dimensional reducible p-adic representations and non-de Rham B-pairs (JAPANESE)

2014年06月17日(火)

17:30-18:30   数理科学研究科棟(駒場) 056号室
Bao Châu Ngô 氏 (University of Chicago, VIASM)
Vinberg's monoid and automorphic L-functions (ENGLISH)
[ 講演概要 ]
We will explain a generalisation of the construction of the local factors of Godement-Jacquet's L-functions, based on Vinberg's monoid.

(本講演は「東京北京パリ数論幾何セミナー」として, インターネットによる東大数理, Morningside Center of MathematicsとIHESの双方向同時中継で行います.)

2014年05月28日(水)

16:40-17:40   数理科学研究科棟(駒場) 056号室
Gantsooj Batzaya 氏 (東京大学数理科学研究科)
On simultaneous approximation to powers of a real number by rational numbers (ENGLISH)

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