2008 Schedule-template for morningside center

各位 同僚:

四月份晨兴算术几何项目将如期开始. 经过和田野,李克正等老师的商量和讨论,我们准备近几年内围绕

"MODULARITY 　AND 　ITS　 APPLICATIONＳ　ＴＯ　ＤＩＯＰＨＡＮＴＩＮＥ　ＥＱＵＡＴＩＯＮＳ＂

开展活动．请大家踊跃参加．

四月份将有以下两个讨论班：

　ＴＡＮＮＡＫＩＡＮ　ＣＡＴＥＧＯＲＩＥＳ　

由丁志国主持．时间每周二下午２：００－５：３０（从４月１起），地点：晨兴４１０．

以下是该讨论班的简要内容：

Ｔhe basic idea to study the Tanakian category is that how one can recover the algebraic groups from their representations. The aim of this seminar try to understand this processe over a field and study the case over Dedekind domain and find some arithmetic application. Some basic and important concept "stack", "gerb" etc will be studied in this seminar. Some basic referernce:

EGA, SGA1,3,4.

Deligne and Milne: Tannakian Categories, in Hodge cycles, Motives and Shimura varieties, LNM900

Deligne: Categories Tannakiennes, in Grothendieck Fest. vol II, P.111-195

Saavedra Rivano: Categories Tannakiennes, LNM265

Breen: Tannakian Categories, Proc.Symp.Pure Math. vol.55 (1994), P.337-376.

ＲＡＴＩＯＮＡＬ　ＰＯＩＮＴＳ　ＡＮＤ　ＩＮＴＥＧＲＡＬ　ＰＯＩＮＴＳ

由魏达盛主持．时间每周三下午２：００－５：３０（从４月９日开始），地点：晨兴４１０．

以下是讨论班的简要内容：

The extensive study of ratioanl points and integral points by using Brauer-Manin obstructions is based on the modularity of GL(1) and

Wiles' proof of Fermat last theorem is based on the modularity of elliptic curves of GL(2) and also Gross-Zagier-Zhang formulae. The aim of this seminar will study various articles on this subject and try to find if there is a more conceptual way to understand such subject. It will also be emphasised to study both rational points and integral points by using L-functions (which is alrady part of modularity) in the seminar.