Colloquium

Seminar information archive ~02/01Next seminarFuture seminars 02/02~

Organizer(s) KATO Akishi, KITAYAMA Takahiro, MITAKE Yoshihiro, TSUJI Takeshi (chair)
URL https://www.ms.u-tokyo.ac.jp/seminar/colloquium/index_e.html

2022/11/25

15:30-16:30   Hybrid
If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please take part online [Reference URL].
Shane Kelly (Graduate School of Mathematical Sciences, the University of Tokyo)
Motivic cohomology: theory and applications
(ENGLISH)
[ Abstract ]
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.
[ Reference URL ]
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZErcumupjouGdXpOac2j3rcFFN545yAuoSb