Motivic Cohomology

Speaker: Nanjun Yang

Time: 08:50 - 10:35, every Wednesday,Friday, 3/16/2022 - 6/8/2022

Venue: 1110

Zoom ID: 638 227 8222PasswordBIMSA


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.



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



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



本人本科毕业于北京航空航天大学,硕士博士毕业于格勒诺布尔-阿尔卑斯大学,博士导师Jean Fasel。之前在丘成桐数学科学中心做博后,现在是BIMSA的助理研究员。本人研究方向为原相(motivic)上同调和周-威特(Chow-Witt)环。本人提出了分裂型米尔诺-威特原相理论并且应用在纤维丛的周-威特环的计算中。相关成果已经独立发表在Manus. Math.Doc. Math.等期刊上。



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