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, as well as the theory of cycle modules. Furthermore, we introduce cancellation theorem, Gysin triangle, projective bundle formula, BB-decomposition and duality.
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, as well as the theory of cycle modules. Furthermore, we introduce cancellation theorem, Gysin triangle, projective bundle formula, BB-decomposition and duality.
讲师
日期
2025年02月18日 至 06月03日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周二 | 09:50 - 12:15 | A3-4-312 | ZOOM 04 | 482 240 1589 | BIMSA |
修课要求
Basic algebraic geometry (GTM 52, Chapter 1-3)
课程大纲
1. Intersection Theory
2. Sheaves with Transfers
3. Milnor K-Theory and Cycle Modules
4. Comparison between Milnor K-Theory and Motivic Cohomology
5. Effective Motivic Categories over Smooth Bases
6. Cancellation Theorem
7. Weight One Motivic Cohomology
8. Comparison between Chow Group and Motivic Cohomology
9. Homotopy Purity, Projective Bundle Theorem, BB-Decomposition and Gysin Triangle
10. Spectra, Symmetric Spectra and Stable Motivic Categories
11. Duality
2. Sheaves with Transfers
3. Milnor K-Theory and Cycle Modules
4. Comparison between Milnor K-Theory and Motivic Cohomology
5. Effective Motivic Categories over Smooth Bases
6. Cancellation Theorem
7. Weight One Motivic Cohomology
8. Comparison between Chow Group and Motivic Cohomology
9. Homotopy Purity, Projective Bundle Theorem, BB-Decomposition and Gysin Triangle
10. Spectra, Symmetric Spectra and Stable Motivic Categories
11. Duality
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).
M. Rost, Chow Groups with Coefficients, Documenta Mathematica (1996), Volume: 1, page 319-393
M. Rost, Chow Groups with Coefficients, Documenta Mathematica (1996), Volume: 1, page 319-393
听众
Graduate
, 博士后
, Researcher
视频公开
公开
笔记公开
不公开
语言
中文
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。研究方向为代数簇的Chow-Witt群。研究成果发表在Camb. J. Math., Ann. K-Theory等期刊上。