18.787 - Topics in Number Theory (Fall 2012)

 

Alternative Title: Abelian Varieties and p-Divisible Groups

Instructor: Sug Woo Shin

Office: Room 2-167

Lectures: TR 1-2:30 LOCATION 2-151

Office Hours: M 10-11, R 2:30-3:30

Email: swshin [at] math . xxx .edu (you know what xxx is)

COURSE DESCRIPTION

A nonempty subset of the following topics will be covered: Basics on group schemes, abelian varieties, p-divisible groups; CM abelian varieties; Dieudonne theory (classification of p-divisible groups in char p up to isogeny); Honda-Tate theory (classification of abelian varieties in char p up to isogeny); Serre-Tate theorem/theory on deformations of p-divisible groups and abelian varieties; Grothendieck-Messing theory on deformations of p-divisible groups; Galois representations associated with abelian varieties; Moduli spaces of abelian varieties

Prerequisites: good background in algebra, number theory and scheme theory

Text Book: There is no official textbook but see the growing references on this website.

RECENT UPDATE

[08.31.2012]  A tentative course website has been created.

[09.08.2012]  The website has been updated.

[09.18.2012]  A link to the typed notes by Holden Lee was created on Schedule page. Problem Sets page was converted to Remarks page.