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Extensions of rank one (φ,Γ)-modules and crystalline representations

Part of: Algebraic number theory: local and $p$-adic fields

Published online by Cambridge University Press:  13 December 2010

Seunghwan Chang  and
Fred Diamond
Seunghwan Chang
Affiliation:
Institute of Mathematical Sciences, Ewha Womans University, Seoul 120-750, Republic of Korea (email: schang@ewha.ac.kr)
Fred Diamond
Affiliation:
Department of Mathematics, King’s College London, Strand, London WC2R 2LS, UK (email: Fred.Diamond@kcl.ac.uk)
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Abstract

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Let K be a finite unramified extension of Qp. We parametrize the (φ,Γ)-modules corresponding to reducible two-dimensional $\overline {\F }_p$-representations of GK and characterize those which have reducible crystalline lifts with certain Hodge–Tate weights.

Keywords

p-adic representationscrystalline representations(φ,Γ)-modulesWach modules

MSC classification

Secondary: 11S25: Galois cohomology

Information

Type
Research Article
Information
Compositio Mathematica , Volume 147 , Issue 2 , March 2011 , pp. 375 - 427
Copyright
Copyright © Foundation Compositio Mathematica 2010

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