Tohoku Mathematical Journal
2005
September
SECOND SERIES VOL. 57, NO. 3

Tohoku Math. J.
57 (2005), 303-319

Title COVARIANT HONDA THEORY

Author Oleg Demchenko

(Received August 21, 2003, revised December 8, 2004)
Abstract. Honda's theory gives an explicit description up to strict isomorphism of formal groups over perfect fields of characteristic $p \neq 0$ and over their rings of Witt vectors by means of attaching a certain matrix, which is called its type, to every formal group. A dual notion of right type connected with the reduction of the formal group is introduced while Honda's original type becomes a left type. An analogue of the Dieudonne module is constructed and an equivalence between the categories of formal groups and right modules satisfying certain conditions, similar to the classical anti-equivalence between the categories of formal groups, and left modules satisfying certain conditions is established. As an application, the $\star$-isomorphism classes of the deformations of a formal group over and the action of its automorphism group on these classes are studied.

2000 Mathematics Subject Classification. Primary 11S31; Secondary 14L05.
Key words and phrases. Formal group, Honda theory, Dieudonné module, $p$-adic period map.

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