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

Published online by Cambridge University Press:  01 January 2008

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 rp−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}.

Type
Research Article
Copyright
Copyright © Foundation Compositio Mathematica 2008