Oberwolfach Seminar: Finite Group Schemes and p-divisible Groups

May 15th - May 21st, 2005
Fabrizio Andreatta, Padova
Brian Conrad, Michigan
Rene Schoof, Rome
Finite group schemes and p-divisible groups are key notions in number theory and arithmetic algebraic geometry. They play an important part in the theory of abelian varieties. The proofs of important number theoretic results such as the Mordell Conjecture (Faltings' Theorem) and the Shimura-Taniyama conjecture make extensive use of the theory of group schemes and p-divisible groups.

In this seminar we present the basic theory of finite group schmemes and p-divisible groups, as well as the theory of Dieudonne' modules and Tate's description of local p-divisible groups. Finite group schemes and p-divisible groups naturally arise in the context of abelian varieties, and we give several applications to the theory of abelian varieties. We deduce Tate's local proof of a formula of Shimura-Taniyama that is fundamental in the theory of complex multiplication, and we obtain a p-adic version of Tate's isogeny theorem on abelian varieties over finite fields. In addition we show how p-divisible groups are used to understand the p-part of the Honda-Tate classification of simple abelian varieties over finite fields (up to isogeny).

Basic commutative algebra and algebraic geometry; familiarity with the basics in the theory of schemes and with the properties of abelian varieties (as in Mumford's book "Abelian Varieties", Ch.2); some familiarity with the theory of central simple algebras.
Deadline for applications:
April 1st, 2005

The seminars take place at the Mathematisches Forschungsinstitut Oberwolfach. The number of participants is restricted to 24. The Institute covers accommodation and food. Travel expenses cannot be reimbursed. Applications including

should be sent as hard copy or by e-mail (.ps or .pdf file) to:

Prof. Dr. Gert-Martin Greuel
Universität Kaiserslautern
Fachbereich Mathematik
Erwin Schrödingerstr.
67663 Kaiserslautern, Germany

Mathematisches Forschungsinstitut Oberwolfach   updated: February 9th, 2009