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Kummer theory for big Galois representations

Published online by Cambridge University Press:  10 April 2007

DANIEL DELBOURGO
Affiliation:
Department of Mathematics, University Park, Nottingham, NG7 2RD. e-mail: [email protected], [email protected]
PAUL SMITH
Affiliation:
Department of Mathematics, University Park, Nottingham, NG7 2RD. e-mail: [email protected], [email protected]

Abstract

In their 1990 paper, Bloch and Kato described the image of the Kummer map on an abelian variety over a local field, as the group of 1-cocycles which trivialise after tensoring by Fontaine's mysterious ring BdR. We prove the analogue of this statement for the universal nearly-ordinary Galois representation. The proof uses a generalisation of the Tate local pairing to representations over affinoid K-algebras.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 2007

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References

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