Hodge-Tate periods and p-adic abelian integrals
In the first part of this paper, the author constructs by explicit computations a natural map from the Tate module of an abelian variety A onto the space of regular 1-forms of the dual of A, thereby obtaining a new proof of results of Tate, Raynaud and Fontaine on the Hodge-Tate decomposition of A in case of good reduction. - In the second part, he uses this map to compute a p-adic analogue of the period pairing on A. The map itself is constructed by a limit process, reminiscent of Mumford's construction of p-adic theta functions [see \textit{P. Norman} (Ph. D., Harvard, 1982), and, for the link with the decomposition, \textit{V. Cristante} in ''Cohomologie p-adique'', Astérisque 119-120, 169-182 (1984; Zbl 0559.14030)].
scientific article; zbMATH DE number 3912530
scientific article