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On lattices in semi-stable representations: a proof of a conjecture of Breuil

Part of: (Co)homology theory Algebraic groups

Published online by Cambridge University Press:  01 January 2008

Tong Liu
Tong Liu*
Affiliation:
Department of Mathematics, University of Pennsylvania, Philadelphia, PA 19104, USA (email: tongliu@math.upenn.edu)
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Abstract

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For p≥3 an odd prime and a nonnegative integer r≤p−2, we prove a conjecture of Breuil on lattices in semi-stable representations, that is, the anti-equivalence of categories between the category of strongly divisible lattices of weight r and the category of Galois stable -lattices in semi-stable p-adic Galois representations with Hodge–Tate weights in {0,…,r}.

Keywords

p-adic representationssemi-stablestrongly divisible lattices

MSC classification

Secondary: 14F30: $p$-adic cohomology, crystalline cohomology 14L05: Formal groups, $p$-divisible groups
Type
Research Article
Information
Compositio Mathematica , Volume 144 , Issue 1 , January 2008 , pp. 61 - 88
Copyright
Copyright © Foundation Compositio Mathematica 2008