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On admissible tensor products in p-adic Hodge theory

Part of: Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  14 February 2013

Giovanni Di Matteo
Giovanni Di Matteo*
Affiliation:
UMPA ENS de Lyon, UMR 5669 du CNRS, Université de Lyon, France (email: giovanni.di.matteo@ens-lyon.fr)
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Abstract

We prove that if W and W′ are non-zero B-pairs whose tensor product is crystalline (or semi-stable or de Rham or Hodge–Tate), then there exists a character μ such that W(μ−1) and W′(μ) are crystalline (or semi-stable or de Rham or Hodge–Tate). We also prove that if W is a B-pair and if F is a Schur functor (for example Sym n or Λn) such that F(W)is crystalline (or semi-stable or de Rham or Hodge–Tate) and if the rank of W is sufficiently large, then there is a character μ such that W(μ−1)is crystalline (or semi-stable or de Rham or Hodge–Tate). In particular, these results apply to p-adic representations.

Keywords

B-paircrystalline representationde Rham representationHodge–Tate representationp-adic Galois representationp-adic Hodge theorySchur functorsemi-stable representationtensor product

MSC classification

Secondary: 11F80: Galois representations

Information

Type
Research Article
Information
Compositio Mathematica , Volume 149 , Issue 3 , March 2013 , pp. 417 - 429
Copyright
Copyright © 2013 The Author(s)

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