Hodge-Tate periods andp-adic abelian integrals

Abstract

Listen

Translate article

The object of this paper is to present two results. The first is a new description of one of the maps involved in the Hodge-Tate decomposit ion of an Abelian variety with good reduction. This result complements recent work of Fontaine IF] and combined with it yields a new proof of this decomposition. The second result is a limit formula involving the integrals described in [C] for what may properly be called Hodge-Tate periods. We will now describe in more detail the contents of this paper. The notations used below are standard and are also explained in Sect. I. Let p be a fixed rational prime. Let II~p be the field of p-adic numbers and ~p the completion of a fixed algebraic closure of II~p. Let A be an Abelian variety defined over a complete discretely valued subfield K of Cp. Let /i denote the dual Abelian variety, and T(A) the p-Tate module of A. Set V(A) = T(A) | 1Igp as a G=Autr The theorem of Tate and Raynaud which describes the decomposit ion of V(A) is equivalent to the following assertion: There exist canonical G-equivariant ~2flinear maps,