理学院专题学术讲座 | Seminar on Algebraic Geometry and Ramification

来源: 发布时间:2021-02-23 作者:

时间:2021年2月25日星期四10:00 - 17:00

Time: 10:00 - 17:00, Thursday, February 25th, 2021

主持人:阳恩林(北京大学),赵以庚(西湖大学)

Host: Dr. Enlin Yang, Peking University and Dr. Yigeng Zhao, Westlake University


1. Speaker: Prof. Will Sawin, Columbia University

Time: 10:00 - 11:00

Online: Zoom Conference (Meeting ID: 633 9213 5002  Passcode: 443384)

Title:Stalks of perverse sheaves in characteristic p

Abstract:Perverse sheaves are objects that efficiently encapsulate geometric information in multiple areas of algebraic geometry, number theory, representation theory, and topology. A key invariant of perverse sheaves is the characteristic cycle, which can be used to calculate the Euler characteristic or the rank of the vanishing cycles at a particular point. Massey showed that the characteristic cycle can be used to bound the stalk of the perverse sheaf at a particular point.

We generalize Massey's formula from characteristic 0 to characteristic p. This relies on the recent construction of the characteristic cycle in characteristic p. It has multiple applications to number theory over the ring of polynomials in one variable over finite fields, since many natural arithmetic functions in that setting arise from the stalks of perverse sheaves - most famously, automorphic forms.


2. Speaker: Dr. Hiroki Kato, Université Paris-Saclay

Time: 16:00 -17:00

Online: Zoom Conference (Meeting ID: 637 8524 5739  Passcode: 375555)

Title: Étale cohomology of rigid analytic varieties via nearby cycles over general bases    

Abstract: One of the most fundamental results in the study of étale cohomology of rigid analytic varieties is the comparison with the nearby cycle cohomology, which gives a canonical isomorphism between the cohomology of an algebraizable rigid analytic variety and the cohomology of the nearby cycle. I will discuss a generalization of this comparison result to the relative case: For an algebraizable morphism, the compactly supported higher direct image sheaves are identified, up to replacing the target by a blowup, with a generalization of the nearby cycle cohomology, which is given by the theory of nearby cycles over general bases. This result can be used to show the existence of a tubular neighborhood that does not change the cohomology for algebraizable families.


欢迎感兴趣的老师、同学参与。

联系人: 西湖大学理学院 杨老师  yanghangli@westlake.edu.cn