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談話会・数理科学講演会
過去の記録 ～11/29｜次回の予定｜今後の予定 11/30～
| 担当者 | 阿部紀行、岩木耕平、河澄響矢（委員長）、小池祐太 |
|---|---|
| セミナーURL | https://www.ms.u-tokyo.ac.jp/seminar/colloquium/index.html |
2022年11月25日(金)
15:30-16:30 ハイブリッド開催
数理科学研究科所属以外の方は、オンラインでのご参加（参考URLから参加登録）をお願いいたします。
Shane Kelly 氏 (東京大学大学院数理科学研究科)
Motivic cohomology: theory and applications
(ENGLISH)
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZErcumupjouGdXpOac2j3rcFFN545yAuoSb
数理科学研究科所属以外の方は、オンラインでのご参加（参考URLから参加登録）をお願いいたします。
Shane Kelly 氏 (東京大学大学院数理科学研究科)
Motivic cohomology: theory and applications
(ENGLISH)
[ 講演概要 ]
The motive of a smooth projective algebraic variety was originally envisaged by Grothendieck in the 60's as a generalisation of the Jacobian of a curve, and formed part of a strategy to prove the Weil conjectures. In the 90s, following conjectures of Beilinson on special values of L-functions, Voevodsky, together with Friedlander, Morel, Suslin, and others, generalised this to the A^1-homotopy type of a general algebraic variety. This A^1-homotopy theory lead to a proof of the Block-Kato conjecture (and a Fields Medal for Voevodsky).
One consequence of making things A^1-invariant is that unipotent groups (as well as wild ramification, irregular singularities, nilpotents including higher nilpotents in the sense of derived algebraic geometry, certain parts of K-theory, etc) become invisible and the last decade has seen a number of candidates for a non-A^1-invariant theory.
In this talk I will give an introduction to the classical theory and discuss some current and future research directions.
[ 参考URL ]The motive of a smooth projective algebraic variety was originally envisaged by Grothendieck in the 60's as a generalisation of the Jacobian of a curve, and formed part of a strategy to prove the Weil conjectures. In the 90s, following conjectures of Beilinson on special values of L-functions, Voevodsky, together with Friedlander, Morel, Suslin, and others, generalised this to the A^1-homotopy type of a general algebraic variety. This A^1-homotopy theory lead to a proof of the Block-Kato conjecture (and a Fields Medal for Voevodsky).
One consequence of making things A^1-invariant is that unipotent groups (as well as wild ramification, irregular singularities, nilpotents including higher nilpotents in the sense of derived algebraic geometry, certain parts of K-theory, etc) become invisible and the last decade has seen a number of candidates for a non-A^1-invariant theory.
In this talk I will give an introduction to the classical theory and discuss some current and future research directions.
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZErcumupjouGdXpOac2j3rcFFN545yAuoSb
