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).
should be sent as hard copy or by e-mail (.ps or .pdf file) to:
Prof. Dr. Gert-Martin Greuel
67663 Kaiserslautern, Germany