数论研讨班

来源:理学院 发布时间:2020-11-16 作者:理学院

时间:2020年11月25日 星期三 9:30-16:00

TimeNovember 25, 2020, Wednesday,9:30-16:00

地点:西湖大学云栖校区4号楼409-411教室

VenueRoom 409-411, Building 4, Yunqi Campus, Westlake University


   1. Speaker: Dr. Yulin Cai, University of Bordeaux

Time: 9:30-11:30

TitleIntegral points on modular curves, singular moduli and conductor-discriminant inequality

AbstractIn the first part, we study S-integral points on the modular curve X0(p). Bilu showed that they can be effectively bounded in terms of p, the base field and the set of places S. Sha made this result explicit, but his bound is double exponential in p. We drastically improve upon the result of Sha, obtaining a simple and explicit exponential bound. This is done using a very explicit version of the Chevalley-Weil principle based on the work of Liu and Lorenzini.

In the second part, we consider singular moduli. For a fixed singular modulus α, we give an effective upper bound of the norm of x−α for another singular modulus x with large discriminant.


In the third part, we give a relation between Artin conductors of a Weierstrass

model Y and the ones of two given Weierstrass models Y1, Y2. With this relation, we know that the conductor-discriminant inequality holds for Y if it holds for Y1 and Y2.


   2. Speaker: Dr. Xiaowen Hu, Sun Yat-sen University

Time: 14:00-16:00

Title: A degeneration formula for tautological sheaves on Hilbert scheme of points

Abstract: First we will give a brief account of Thomason's Lefschetz-Riemann-Roch theorem, and the theory of algebraic cobordism. Inspired by Wang-Zhou and Krug's conjecture, it suggests a degeneration formula, or a so-called inclusion-exclusion principle for Euler characteristic of tautological sheaves on Hilbert scheme of points. Then I will outline a proof using Li-Wu's theory of good degeneration and its GIT construction by Gulbrandsen-Halle-Hulek.



欢迎感兴趣的老师、同学参加,并共同讨论。


组织者:赵以庚

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