THE THEORY OF COMMUTATIVE FORMAL GROUPS OVER FIELDS OF FINITE CHARACTERISTIC

Abstract

CONTENTS Introduction Chapter I. Formal groups and Dieudonné modules; basic concepts 1. Groups in categories 2. Algebraic and formal groups. Bialgebras 3. The structure of commutative artinian groups 4. The Dieudonné module of a formal group 5. Comments Chapter II. Dieudonné modules; classification up to isogeny 1. Reduction of the problem 2. Modules over the ring A 3. A technical result 4. Classification of formal groups up to isogeny 5. Comments Chapter III. Dieudonné modules; classification up to isomorphism 1. Statement of the problem 2. Auxiliary results 3. The algebraic structure on the module space 4. The structure of isosimple modules; subsidiary reduction 5. The structure of isosimple modules; proof of the first finiteness theorem 6. The second finiteness theorem 7. Cyclic isosimple modules; the component of maximal dimension 8. Classification of two-dimensional modules 9. Comments Chapter IV. Algebroid formal groups and abelian varieties 1. General results 2. The formal structure of abelian varieties; preliminary reduction 3. The formal structure of abelian varieties; the fundamental theorem 4. Weakly algebroid groups 5. Remarks and examples 6. Comments References