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日時: 2022年11月25日(金) 15:30-16:30
Date: November 25, 2022 15:30-16:30
会場:東京大学大学院数理科学研究科 大講義室（ハイブリッド開催）
Place: Lecture Room, Graduate School of Math. Sci. Bldg.(zoom hybrid)
Shane Kelly 氏（東京大学大学院数理科学研究科）
Shane Kelly (Graduate School of Mathematical Sciences, The University of Tokyo)
Motivic cohomology: theory and applications (ENGLISH)
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.