Introduction to the Theory of Formal Groups

This volume, starts with the concept of C-group for any category C (with products and final object), but the author’s do not exploit it in its full generality. The book is meant to be introductory to the theory, and therefore the necessary background to its minimum possible level is minimised.

Foreword -- Notations -- Chapter I DEFINITION OF FORMAL GROUPS -- §1. C-groups and C-cogroups -- §2. Formal groups and their bigebras -- §3. Elementary theory of formal groups -- Chapter II INFINITESIMAL FORMAL GROUPS -- §1. The decomposition theorem -- §2. The structure theorem for stable infinitesimal formal groups -- §3. Reduced infinitesimal formal groups -- Chapter III INFINITESIMAL COMMUTATIVE GROUPS -- §1. Generalities -- §2. Free commutative bigebras -- §3. Modules of hyperexponential vectors -- §4. Distinguished modules over a Hilbert-Wittring -- §5. The case of an algebraically closed field -- §6. Applications to commutative reduced infinitesimal groups -- Chapter IV REPRESENTABLE REDUCED INFINITESIMAL GROUPS -- Bibliography -- Index.

Dieudonne\, Jean A.