Hodge-Tate periods and p-adic abelian integrals
type: Item
instance of: scholarly article
title: Hodge-Tate periods and p-adic abelian integrals
zbMATH Open document ID: 0572.14024
DOI: 10.1007/BF01388442
author: Robert F. Coleman
published in: Inventiones Mathematicae
publication date: 1984-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143177
review text: 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)].
Mathematics Subject Classification ID: 14K15
Mathematics Subject Classification ID: 14F30
Mathematics Subject Classification ID: 14K20
zbMATH DE Number: 3912530
zbMATH Keywords: De Rham cohomology
zbMATH Keywords: Tate module of an abelian variety
zbMATH Keywords: regular 1-forms
reviewed by: Daniel Bertrand
MaRDI profile type: Publication
cites work: On Primes of Degree One in Function Fields
cites work: Formes différentielles et modules de Tate des variétés abéliennes sur les corps locaux. (Différential forms and Tate modules of abelian varieties over local fields)
cites work: Über Restklassennormen auf affinoiden Algebren
cites work: Critères de platitude et de projectivité. Techniques de ''platification'' d'un module. (Criterial of flatness and projectivity. Technics of ''flatification of a module.)
cites work: Q3663443
cites work: Q5628266
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description: scientific article; zbMATH DE number 3912530