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Kummer theory for big Galois representations

Published online by Cambridge University Press:  10 April 2007

DANIEL DELBOURGO  and
PAUL SMITH
DANIEL DELBOURGO
Affiliation:
Department of Mathematics, University Park, Nottingham, NG7 2RD. e-mail: dd@maths.nott.ac.uk, pmxpas@maths.nott.ac.uk
PAUL SMITH
Affiliation:
Department of Mathematics, University Park, Nottingham, NG7 2RD. e-mail: dd@maths.nott.ac.uk, pmxpas@maths.nott.ac.uk
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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 B dR. 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.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 142 , Issue 2 , March 2007 , pp. 205 - 217
Copyright
Copyright © Cambridge Philosophical Society 2007

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References

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