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代数学コロキウム
過去の記録 ～12/07｜次回の予定｜今後の予定 12/08～
| 開催情報 | 水曜日 17:00～18:00 数理科学研究科棟(駒場) 117号室 |
|---|---|
| 担当者 | 今井 直毅，ケリー シェーン |
過去の記録
2008年08月01日(金)
13:00-18:00 数理科学研究科棟(駒場) 002号室
4講演あります.また,いつもと曜日,時間,場所が異なります.
ご注意下さい.
Olivier Brinon 氏 (Paris北大学) 13:00-14:00
B_dR-representations and Higgs bundles
Henrik Russell 氏 (Duisburg-Essen大学) 14:15-15:15
Generalized Albanese and duality
Thomas Geisser 氏 (南California大学) 15:45-16:45
Negative K-theory, homotopy invariance and regularity
On Iwasawa theory for abelian varieties over function fields of positive characteristic
4講演あります.また,いつもと曜日,時間,場所が異なります.
ご注意下さい.
Olivier Brinon 氏 (Paris北大学) 13:00-14:00
B_dR-representations and Higgs bundles
Henrik Russell 氏 (Duisburg-Essen大学) 14:15-15:15
Generalized Albanese and duality
Thomas Geisser 氏 (南California大学) 15:45-16:45
Negative K-theory, homotopy invariance and regularity
[ 講演概要 ]
The topic of my talk are two classical conjectures in K-theory:
Weibel's conjecture states that a scheme of dimension d
has no K-groups below degree -d, and Vorst's conjecture
states that homotopy invariance of the K-theory of rings
implies that the ring must be regular.
I will give an easy introduction to the conjectures, and discuss
recent progress.
Fabien Trihan 氏 (Nottingham大学) 17:00-18:00The topic of my talk are two classical conjectures in K-theory:
Weibel's conjecture states that a scheme of dimension d
has no K-groups below degree -d, and Vorst's conjecture
states that homotopy invariance of the K-theory of rings
implies that the ring must be regular.
I will give an easy introduction to the conjectures, and discuss
recent progress.
On Iwasawa theory for abelian varieties over function fields of positive characteristic
2008年07月16日(水)
16:30-17:30 数理科学研究科棟(駒場) 117号室
Valentina Di Proietto 氏 (Padova大学)
On p-adic differential equation on semi-stable varieties
Valentina Di Proietto 氏 (Padova大学)
On p-adic differential equation on semi-stable varieties
2008年07月02日(水)
16:30-17:30 数理科学研究科棟(駒場) 117号室
近藤 智 氏 (東京大学数物連携宇宙研究機構)
有限体上のスキームのふたつのモチビックコホモロジー群の計算
(安田正大氏との共同研究)
近藤 智 氏 (東京大学数物連携宇宙研究機構)
有限体上のスキームのふたつのモチビックコホモロジー群の計算
(安田正大氏との共同研究)
2008年06月18日(水)
16:30-18:45 数理科学研究科棟(駒場) 117号室
服部 新 氏 (北海道大学大学院理学研究院) 16:30-17:30
On a ramification bound of semi-stable torsion representations over a local field
朝倉 政典 氏 (北海道大学大学院理学研究院) 17:45-18:45
Beilinson-Tate予想と楕円曲面のK_1の不分解元
服部 新 氏 (北海道大学大学院理学研究院) 16:30-17:30
On a ramification bound of semi-stable torsion representations over a local field
朝倉 政典 氏 (北海道大学大学院理学研究院) 17:45-18:45
Beilinson-Tate予想と楕円曲面のK_1の不分解元
[ 講演概要 ]
(佐藤周友氏との共同研究)
代数サイクルのTate予想のK理論における類似であるBeilinson-Tate予想について、
楕円曲面の場合にそれが成り立つ非自明な例を構成する。
これは、p進レギュレーターの非消滅と関係しており、
応用としてK_1の不分解元であって整数環上のモデルからくるようなものを構成する。
(佐藤周友氏との共同研究)
代数サイクルのTate予想のK理論における類似であるBeilinson-Tate予想について、
楕円曲面の場合にそれが成り立つ非自明な例を構成する。
これは、p進レギュレーターの非消滅と関係しており、
応用としてK_1の不分解元であって整数環上のモデルからくるようなものを構成する。
2008年06月04日(水)
16:30-17:30 数理科学研究科棟(駒場) 117号室
坂内 健一 氏 (慶應義塾大学理工学部 )
$p$-adic elliptic polylogarithm, $p$-adic Eisenstein series and Katz measure
(joint work with G. Kings)
坂内 健一 氏 (慶應義塾大学理工学部 )
$p$-adic elliptic polylogarithm, $p$-adic Eisenstein series and Katz measure
(joint work with G. Kings)
[ 講演概要 ]
The Eisenstein classes are important elements in the motivic cohomology
of a modular curve, defined as the specializations of the motivic elliptic
polylogarithm by torsion sections. The syntomic Eisenstein classes are
defined as the image by the syntomic regulator of the motivic Eisenstein
classes. In this talk, we explain our result concerning the relation between
syntomic Eisenstein classes restricted to the ordinary locus and
p-adic Eisenstein series.
The Eisenstein classes are important elements in the motivic cohomology
of a modular curve, defined as the specializations of the motivic elliptic
polylogarithm by torsion sections. The syntomic Eisenstein classes are
defined as the image by the syntomic regulator of the motivic Eisenstein
classes. In this talk, we explain our result concerning the relation between
syntomic Eisenstein classes restricted to the ordinary locus and
p-adic Eisenstein series.
2008年05月07日(水)
16:30-17:30 数理科学研究科棟(駒場) 117号室
今井 直毅
氏 (東京大学大学院数理科学研究科)
On the connected components of moduli spaces of finite flat models
今井 直毅
氏 (東京大学大学院数理科学研究科)
On the connected components of moduli spaces of finite flat models
2008年04月30日(水)
16:30-17:30 数理科学研究科棟(駒場) 117号室
原 隆 氏 (東京大学大学院数理科学研究科)
Iwasawa theory of totally real fields for certain non-commutative $p$-extensions
原 隆 氏 (東京大学大学院数理科学研究科)
Iwasawa theory of totally real fields for certain non-commutative $p$-extensions
[ 講演概要 ]
Recently, Kazuya Kato has proven the non-commutative Iwasawa main
conjecture (in the sense of Coates, Fukaya, Kato, Sujatha and Venjakob) for
non-commutative Galois extensions of "Heisenberg type" of totally real fields,
using integral logarithmic homomorphisms. In this talk, we apply Kato's method
to certain non-commutative $p$-extensions which are more complicated than those
of Heisenberg type, and prove the main conjecture for them.
Recently, Kazuya Kato has proven the non-commutative Iwasawa main
conjecture (in the sense of Coates, Fukaya, Kato, Sujatha and Venjakob) for
non-commutative Galois extensions of "Heisenberg type" of totally real fields,
using integral logarithmic homomorphisms. In this talk, we apply Kato's method
to certain non-commutative $p$-extensions which are more complicated than those
of Heisenberg type, and prove the main conjecture for them.
2008年01月30日(水)
16:30-17:30 数理科学研究科棟(駒場) 117号室
Luc Illusie 氏 (Universite Paris-Sud 11)
Odds and ends on finite group actions and traces
Luc Illusie 氏 (Universite Paris-Sud 11)
Odds and ends on finite group actions and traces
[ 講演概要 ]
Suppose a finite group G acts on a scheme X separated and of finite type over a field k. This raises several questions about the traces of elements s of G (or more generally products sg, for g in the Galois group of k) on cohomology groups of various types associated with X/k (with compact support or no support, Betti if k = C, l-adic, rigid). Some were considered and solved long ago, others only recently. I will in particular discuss an equivariant generalization of a theorem of Laumon on Euler-Poincar¥'e characteristics.
Suppose a finite group G acts on a scheme X separated and of finite type over a field k. This raises several questions about the traces of elements s of G (or more generally products sg, for g in the Galois group of k) on cohomology groups of various types associated with X/k (with compact support or no support, Betti if k = C, l-adic, rigid). Some were considered and solved long ago, others only recently. I will in particular discuss an equivariant generalization of a theorem of Laumon on Euler-Poincar¥'e characteristics.
2008年01月23日(水)
16:30-17:30 数理科学研究科棟(駒場) 117号室
Weizhe Zheng 氏 (Universite Paris-Sud 11)
Integrality, Rationality, and Independence of l in l-adic Cohomology over Local Fields
Weizhe Zheng 氏 (Universite Paris-Sud 11)
Integrality, Rationality, and Independence of l in l-adic Cohomology over Local Fields
[ 講演概要 ]
I will discuss two problems on traces in l-adic cohomology over local fields with finite residue field. In the first part, I will describe the behavior of integral complexes of l-adic sheaves under Grothendieck's six operations and the nearby cycle functor. In the second part, I will talk about rationality and independence of l. More precisely, I will introduce a notion of compatibility for systems of l-adic complexes and explain the proof of its stability by the above operations, in a slightly more general context (equivariant under finite groups). The main tool in this talk is a theorem of de Jong on
alterations.
I will discuss two problems on traces in l-adic cohomology over local fields with finite residue field. In the first part, I will describe the behavior of integral complexes of l-adic sheaves under Grothendieck's six operations and the nearby cycle functor. In the second part, I will talk about rationality and independence of l. More precisely, I will introduce a notion of compatibility for systems of l-adic complexes and explain the proof of its stability by the above operations, in a slightly more general context (equivariant under finite groups). The main tool in this talk is a theorem of de Jong on
alterations.
2008年01月16日(水)
16:30-17:30 数理科学研究科棟(駒場) 117号室
Antoine Chambert-Loir 氏 (Universite de Rennes 1)
Equidistribution theorems in Arakelov geometry
Antoine Chambert-Loir 氏 (Universite de Rennes 1)
Equidistribution theorems in Arakelov geometry
[ 講演概要 ]
The proof of Bogomolov's conjecture by Zhang made a crucial use
of an equidistribution property for the Galois orbits of points of small
heights in Abelian varieties defined over number fields.
Such an equidistribution property is proved using a method invented
by Szpiro, Ullmo and Zhang, and makes use of Arakelov theory.
This equidistribution theorem takes place in the complex torus
associated to the Abelian variety. I will show how a similar
equidistribution theorem can be proven for the p-adic topology ;
we have to use Berkovich space. Thanks to recent results of Yuan
about `big line bundles' in Arakelov geometry, the situation
is now very well understood.
The proof of Bogomolov's conjecture by Zhang made a crucial use
of an equidistribution property for the Galois orbits of points of small
heights in Abelian varieties defined over number fields.
Such an equidistribution property is proved using a method invented
by Szpiro, Ullmo and Zhang, and makes use of Arakelov theory.
This equidistribution theorem takes place in the complex torus
associated to the Abelian variety. I will show how a similar
equidistribution theorem can be proven for the p-adic topology ;
we have to use Berkovich space. Thanks to recent results of Yuan
about `big line bundles' in Arakelov geometry, the situation
is now very well understood.
2007年12月05日(水)
16:30-17:30 数理科学研究科棟(駒場) 117号室
中村健太郎 氏 (東京大学大学院数理科学研究科)
Classification of two dimensional trianguline representations of p-adic fields
中村健太郎 氏 (東京大学大学院数理科学研究科)
Classification of two dimensional trianguline representations of p-adic fields
[ 講演概要 ]
Trianguline representation is a class of p-adic Galois representations of p-adic fields. This was defined by P.Colmez by using ($\\varphi, \\Gamma$)-modules over Robba ring. In his study of p-adic local Langlands correspondence of GL_2(Q_p), he completely classified two dimensional trianguline representations of Q_p. On the other hand, L.Berger recently defined the category of B-pairs and established the equivalence between the category of B-pairs and the category of ($\\varphi,\\Gamma$)-modules over Robba ring. In this talk, we extend the Colmez's result by using B-pairs. We completely classify two dimensional trianguline representations of K for any finite extension of Q_p. We also talk about a relation between two dimensional trianguline representations and principal series or special series of GL_2(K).
Trianguline representation is a class of p-adic Galois representations of p-adic fields. This was defined by P.Colmez by using ($\\varphi, \\Gamma$)-modules over Robba ring. In his study of p-adic local Langlands correspondence of GL_2(Q_p), he completely classified two dimensional trianguline representations of Q_p. On the other hand, L.Berger recently defined the category of B-pairs and established the equivalence between the category of B-pairs and the category of ($\\varphi,\\Gamma$)-modules over Robba ring. In this talk, we extend the Colmez's result by using B-pairs. We completely classify two dimensional trianguline representations of K for any finite extension of Q_p. We also talk about a relation between two dimensional trianguline representations and principal series or special series of GL_2(K).
2007年11月21日(水)
16:30-17:30 数理科学研究科棟(駒場) 117号室
Christopher Rasmussen 氏 (京都大学数理解析研究所)
Abelian varieties with constrained torsion
Christopher Rasmussen 氏 (京都大学数理解析研究所)
Abelian varieties with constrained torsion
[ 講演概要 ]
The pro-$l$ Galois representation attached to the arithmetic fundamental group of a curve $X$ is heavily influenced by the arithmetic of certain classes of its branched covers. It is natural, therefore, to search for and classify these special covers in a meaningful way. When $X$ is the projective line minus three points, one finds that such covers are very scarce. In joint work with Akio Tamagawa, we formulate a conjecture to quanitify this scarcity, and present a proof for the conjecture in the case of genus one curves defined over $\\Q$.
The pro-$l$ Galois representation attached to the arithmetic fundamental group of a curve $X$ is heavily influenced by the arithmetic of certain classes of its branched covers. It is natural, therefore, to search for and classify these special covers in a meaningful way. When $X$ is the projective line minus three points, one finds that such covers are very scarce. In joint work with Akio Tamagawa, we formulate a conjecture to quanitify this scarcity, and present a proof for the conjecture in the case of genus one curves defined over $\\Q$.
2007年10月31日(水)
16:30-17:30 数理科学研究科棟(駒場) 117号室
Pierre Colmez 氏 (Ecole Polytechnique)
On the p-adic local Langlands correspondance for GL2(Qp)
Pierre Colmez 氏 (Ecole Polytechnique)
On the p-adic local Langlands correspondance for GL2(Qp)
2007年10月24日(水)
16:30-17:30 数理科学研究科棟(駒場) 117号室
阿部知行 氏 (東京大学大学院数理科学研究科)
l進層のSwan導手とunit-root
overconvergent F-isocrystalの特性サイクルについて
阿部知行 氏 (東京大学大学院数理科学研究科)
l進層のSwan導手とunit-root
overconvergent F-isocrystalの特性サイクルについて
[ 講演概要 ]
今回の講演ではBerthelotによる数論的D加群の理論を用いることによってunit-root overconvergent F-isocrystalに対してSwan導手を定義し、Kato-Saitoにより幾何学的な手法を用いて定義されたSwan導手と比較する。応用として、特異点の解消の仮定のもとでKato-SaitoのSwan導手の整数性予想を導く。
今回の講演ではBerthelotによる数論的D加群の理論を用いることによってunit-root overconvergent F-isocrystalに対してSwan導手を定義し、Kato-Saitoにより幾何学的な手法を用いて定義されたSwan導手と比較する。応用として、特異点の解消の仮定のもとでKato-SaitoのSwan導手の整数性予想を導く。
2007年10月10日(水)
16:30-17:30 数理科学研究科棟(駒場) 117号室
代数幾何学セミナーとの合同講演会です
James Lewis 氏 (University of Alberta)
Abel-Jacobi Maps Associated to Algebraic Cycles I
代数幾何学セミナーとの合同講演会です
James Lewis 氏 (University of Alberta)
Abel-Jacobi Maps Associated to Algebraic Cycles I
[ 講演概要 ]
This talk concerns the Bloch cycle class map from the higher Chow groups to Deligne cohomology of a projective algebraic manifold. We provide an explicit formula for this map in terms of polylogarithmic type currents.
This talk concerns the Bloch cycle class map from the higher Chow groups to Deligne cohomology of a projective algebraic manifold. We provide an explicit formula for this map in terms of polylogarithmic type currents.
2007年09月19日(水)
16:30-17:30 数理科学研究科棟(駒場) 117号室
Gereon Quick 氏 (Universitaet Muenster)
Etale cobordism
Gereon Quick 氏 (Universitaet Muenster)
Etale cobordism
[ 講演概要 ]
We define and study a new candidate of etale topological cohomology theories for schemes over a field of abritrary characteristic: etale cobordism. As etale K-theory is related to algebraic K-theory, etale cobordism is related to algebraic cobordism of Voevodsky and Levine/Morel. It shares some nice properties of topological theories, e.g. it is equipped with an Atiyah-Hirzebruch spectral sequence from etale cohomology. We discuss in particular a comparison theorem between etale and algebraic cobordism after inverting a Bott element and, finally, we give an outlook to further possible applications of this theory.
We define and study a new candidate of etale topological cohomology theories for schemes over a field of abritrary characteristic: etale cobordism. As etale K-theory is related to algebraic K-theory, etale cobordism is related to algebraic cobordism of Voevodsky and Levine/Morel. It shares some nice properties of topological theories, e.g. it is equipped with an Atiyah-Hirzebruch spectral sequence from etale cohomology. We discuss in particular a comparison theorem between etale and algebraic cobordism after inverting a Bott element and, finally, we give an outlook to further possible applications of this theory.
2007年09月12日(水)
15:00-18:00 数理科学研究科棟(駒場) 117号室
代数幾何学セミナーとの合同講演会です
E. Lau 氏 (Univ. of Bielefeld) 15:00-15:45
Classification of p-divisible groups by displays and duality
T. Zink 氏 (Univ. of Bielefeld) 16:00-16:45
Applications of the theory of displays
E. Looijenga 氏 (Univ. of Utrecht) 17:00-18:00
Presentation of mapping class groups from algebraic geometry
代数幾何学セミナーとの合同講演会です
E. Lau 氏 (Univ. of Bielefeld) 15:00-15:45
Classification of p-divisible groups by displays and duality
T. Zink 氏 (Univ. of Bielefeld) 16:00-16:45
Applications of the theory of displays
E. Looijenga 氏 (Univ. of Utrecht) 17:00-18:00
Presentation of mapping class groups from algebraic geometry
[ 講演概要 ]
A presentation of the mapping class group of a genus g surface with one hole is due to Wajnryb with later improvements due to M. Matsumoto. The generators are Dehn twists defined by 2g+1 closed curves on the surface. The relations involving only two Dehn twists are the familiar Artin relations, we show that those involving more than two can be derived from algebro-geometry considerations.
A presentation of the mapping class group of a genus g surface with one hole is due to Wajnryb with later improvements due to M. Matsumoto. The generators are Dehn twists defined by 2g+1 closed curves on the surface. The relations involving only two Dehn twists are the familiar Artin relations, we show that those involving more than two can be derived from algebro-geometry considerations.
2007年08月27日(月)
16:30-17:30 数理科学研究科棟(駒場) 002号室
Steven Zucker 氏 (Johns Hopkins大学)
The reductive Borel-Serre motive
Steven Zucker 氏 (Johns Hopkins大学)
The reductive Borel-Serre motive
2007年07月18日(水)
16:30-17:30 数理科学研究科棟(駒場) 117号室
梶原 健 氏 (横浜国立大学)
Tropical toric varieties
梶原 健 氏 (横浜国立大学)
Tropical toric varieties
2007年07月11日(水)
16:30-17:30 数理科学研究科棟(駒場) 117号室
Andreas Rosenschon 氏 (University of Alberta)
Algebraic cycles on products of elliptic curves over p-adic fields
Andreas Rosenschon 氏 (University of Alberta)
Algebraic cycles on products of elliptic curves over p-adic fields
2007年06月27日(水)
16:30-17:30 数理科学研究科棟(駒場) 117号室
Stephen Lichtenbaum 氏 (Brown University)
The conjecture of Birch and Swinnerton-Dyer is misleading
Stephen Lichtenbaum 氏 (Brown University)
The conjecture of Birch and Swinnerton-Dyer is misleading
[ 講演概要 ]
All values of zeta and L-functions at integral points should be given in terms of products and quotients of Euler characteristics, and the order of the zeroes and poles at these
points should be given by the sum and difference of the ranks of
corresponding finitely generated abelian groups.
All values of zeta and L-functions at integral points should be given in terms of products and quotients of Euler characteristics, and the order of the zeroes and poles at these
points should be given by the sum and difference of the ranks of
corresponding finitely generated abelian groups.
2007年05月09日(水)
16:30-17:30 数理科学研究科棟(駒場) 117号室
宮崎 直 氏 (東京大学大学院数理科学研究科)
$(g,K)$-module structures of principal series representations
of $Sp(3,R)$
宮崎 直 氏 (東京大学大学院数理科学研究科)
$(g,K)$-module structures of principal series representations
of $Sp(3,R)$
2007年05月02日(水)
16:30-17:30 数理科学研究科棟(駒場) 117号室
長谷川 泰子 氏 (東京大学大学院数理科学研究科)
Cohen-Eisenstein series and modular forms associated to imaginary quadratic fields
長谷川 泰子 氏 (東京大学大学院数理科学研究科)
Cohen-Eisenstein series and modular forms associated to imaginary quadratic fields
2007年04月25日(水)
16:30-17:30 数理科学研究科棟(駒場) 117号室
津嶋 貴弘 氏 (東京大学大学院数理科学研究科)
Localized Characteristic Class and Swan Class
津嶋 貴弘 氏 (東京大学大学院数理科学研究科)
Localized Characteristic Class and Swan Class
2007年04月11日(水)
16:30-17:30 数理科学研究科棟(駒場) 117号室
斎藤 毅 氏 (東京大学大学院数理科学研究科)
l進層の暴分岐と特性サイクル
斎藤 毅 氏 (東京大学大学院数理科学研究科)
l進層の暴分岐と特性サイクル
