Group schemes, formal groups, and p-divisible groups.

*(English)*Zbl 0603.14033
Arithmetic geometry, Pap. Conf., Storrs/Conn. 1984, 29-78 (1986).

[For the entire collection see Zbl 0596.00007.]

This article is intended to be an introduction to the (highly sophisticated) theory referred to in the title. It begins with some general facts about group schemes and then studies the finite group schemes. Although this paper is a survey, the author presents in this part also some original results concerning the Sylow group schemes. Then one studies thoroughly the commutative finite group schemes. Next one develops those general facts about formal groups that are needed in the last part of the paper, which deals with the p-divisible groups (which are a special kind of formal groups). Many important results on p- divisible groups (due especially to J. Tate) which are relevant to arithmetic questions, are presented. The reader can find throughout the paper a lot of examples illustrating the theory developed. Although the proofs of some important results are skipped (in fact full details would require a whole book itself), many other proofs are however included.

This article is intended to be an introduction to the (highly sophisticated) theory referred to in the title. It begins with some general facts about group schemes and then studies the finite group schemes. Although this paper is a survey, the author presents in this part also some original results concerning the Sylow group schemes. Then one studies thoroughly the commutative finite group schemes. Next one develops those general facts about formal groups that are needed in the last part of the paper, which deals with the p-divisible groups (which are a special kind of formal groups). Many important results on p- divisible groups (due especially to J. Tate) which are relevant to arithmetic questions, are presented. The reader can find throughout the paper a lot of examples illustrating the theory developed. Although the proofs of some important results are skipped (in fact full details would require a whole book itself), many other proofs are however included.

Reviewer: L.Bădescu