Motivic Cohomology
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.
讲师
日期
2022年03月16日 至 06月08日
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修课要求
Basic algebraic geometry (GTM 52, Chapter 1-3)
参考资料
C. Mazza, V. Voevodsky, C. Weibel, Lecture Notes on Motivic Cohomology, American Mathematical Society, Providence, RI, for the Clay Mathematics Institute, Cambridge, MA (2006).
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讲师介绍
杨南君，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。之后在丘成桐数学科学中心做博后，现在是BIMSA的助理研究员。研究方向为原相（motivic）上同调和周-威特（Chow-Witt）环。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Camb. J. Math.和Doc. Math.等期刊上。