Motivic Cohomology in 2022

Motivic cohomology, originated from Deligne, Beilinson and Lichtenbaum and developed by Voevodsky, is a kind of cohomology theory on schemes. It admits comparison with étale cohomology of powers of roots of unity (Beilinson-Lichtenbaum), together with higher Chow groups, and relates to K-theory by Atiyah-Hirzebruch spectral sequence. In this lecture, we establish the category of motives in which the motivic cohomologies are realized. We explain its relationship with Milnor K-theory and Chow group. Furthermore, we introduce devices like MV-sequence, Gysin triangle, projective bundle formula and duality.

Lecturer

Nanjun Yang

Date

16th March ~ 8th June, 2022

Website

http://www.bimsa.cn/newsinfo/601293.html

Prerequisite

Basic algebraic geometry (GTM 52, Chapter 1-3)

Reference

C. Mazza, V. Voevodsky, C. Weibel, Lecture Notes on Motivic Cohomology, American Mathematical Society, Providence, RI, for the Clay Mathematics Institute, Cambridge, MA (2006).

Video Public

Yes

Notes Public

Yes

Lecturer Intro

Nanjun Yang got his doctor and master degree in University of Grenoble-Alpes, advised by Jean Fasel, and bachelor degree in Beihang University. Then he became a postdoc in YMSC. Currently he is a assistant professor in BIMSA. His research interest is the Chow-Witt group of algebraic varieties, with publications on journals such as Camb. J. Math and Ann. K-Theory.