BIMSA > Steenrod Operations: From Classical to Motivic \(ICBS\)
Steenrod Operations: From Classical to Motivic
Steenrod operations are natural transformations of cohomology groups of spaces being compatible with suspensions, which play an important role especially in homotopy theory, for example, the Hopf invariant one problem and Adams spectral sequence. In this course, we introduce the Steenrod operations for both singular cohomologies and motivic cohomologies, focusing on constructions and basic properties. In particular, we prove the Adem relations and give the Hopf algebra (algebroid) structure of Steenrod algebra and its dual.
Professor Lars Aake Andersson
讲师
杨南君
日期
2024年09月20日 至 2025年01月10日
位置
Weekday Time Venue Online ID Password
周五 09:50 - 12:15 Shuangqing-B626 ZOOM 01 928 682 9093 BIMSA
修课要求
Algebraic topology and algebraic geometry
课程大纲
1. Classical Steenrod operations
2. Classical Steenrod algebra and its dual
3. Equidimensional cycles
4. Motivic Steenrod operations
5. Motivic Steenrod algebra and its dual
参考资料
O. Pushin, Steenrod operations in motivic cohomology, thesis
G. Powell, Steenrod operations in motivic cohomology, Luminy lecture notes
J. Riou, Opérations de Steenrod motiviques, arXiv:1207.3121v1
C. Mazza, V. Voevodsky, C. Weibel, Lecture notes on motivic cohomology, American Mathematical Society, Providence, RI, for the Clay Mathematics Institute, Cambridge, MA (2006).
A. Suslin and V. Voevodsky, Relative cycles and Chow sheaves, Annals of Mathematical Studies, vol. 143, Princeton University Press, 2000
A. Hatcher, Algebraic topology
听众
Graduate , 博士后 , Researcher
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笔记公开
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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。