首都师范大学算术几何讨论班（2017-2-28）

[xu...@math.ac.cn]

诸位:

新年好！欢迎参加下周首师大算术几何讨论班。

时间：2017年2月28日（周二）下午 4:30-5:30

地点：首都师范大学校本部新教二楼（数学院新楼）509教室（地铁6号线花园桥站西南出口）

报告人：阳恩林（德国Regensburg大学）

题目：Twist formula for the epsilon factor of a constructible etale sheaf.

摘要: Recently, the singular support and the characteristic cycle of a constructible
sheaf on a smooth  variety over an arbitrary perfect field are constructed by Beilinson and Saito respectively. Based on their theory, we proved a twist formula for the epsilon factor of a constructible sheaf on a projective smooth variety over a finite field in terms of characteristic class of the sheaf. This formula was conjectured by Kato and Saito in 2004.
As a corollary of our formula, we showed that the characteristic classes of 
constructible etale sheaves on projective smooth varieties over a finite field are compatible with proper push-forward. This is a joint work with Naoya Umezaki and Yigeng Zhao.

祝好！

徐飞

[xu...@math.ac.cn]

诸位：

 

本周数论与代数几何讨论班：

 

报告人：张磊博士（德国柏林自由大学）

时间：3月30日（星期四）下午4:30-5:30

 

地点：本部新教二楼610教室

题目: The Nori fundamental gerbe

摘要: In the paper "The Nori fundamental gerbe of a fibered category" N. Borne and A. Vistoli generalized the notion of Nori fundamental group on schemes to that of Nori fundamental gerbe on  fibered categories, and they gave a Tannakian interpretation of the fundamental gerbe when the fibered category is pseudo-poper. Here a fibered category X is called  "pseudo-poper" if it is quasi-compact and if the space of global sections of any vector bundle on X is a finite dimensional vector space. This is not a significant generalization if the fibered category is a scheme, but it is so when we consider stacks. In fact this notion includes a large class of extremely important stacks, namely the affine gerbes. In the leture we will first introduce the techniques developped by Borne-Vistoli, then we will introduce a generalization of the Tannakian interpretation to non pseudo-proper fibered categories which is due to Fabio Tonini and me.  In the end we will also introduce a Lange und Stuhler style theorem for algebraic stacks which roughly says that a vector bundle comes from the representation of the fundamental group if and only if it is trivialized by a finite surjective cover. We managed to do this for even non pseudo-proper algebraic stacks.

 

欢迎参加！

 

 

徐飞

[xu...@math.ac.cn]

诸位：

 

下周数论与代数几何讨论班：

报告人：陈猛教授（复旦大学）

时间：4月7日（星期五）下午4:30-5:30

地点：本部新教二楼725教室

题目:  具有较大体积的射影簇的典范稳定性递归猜想

摘要:  设 n 是一个正整数，典范稳定性递归猜想认为：对于体积足够大的 n 维射影簇 X，其典范稳定性指数 r_s(X) 小于或等于第 n-1 个典范稳定性指数 r_{n-1}。在这个报告中，我们介绍当 n 小于或等于 5 时这个猜想的证明方法和其它弱形式。

 

欢迎参加！

 

 

徐飞