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1 results

  • On admissible tensor products in p-adic Hodge theory

  • Part of
  • Giovanni Di Matteo
  • Journal:
    Compositio Mathematica / Volume 149 / Issue 3 / March 2013
    Published online by Cambridge University Press:
    14 February 2013, pp. 417-429
    Print publication:
    March 2013
    • Article
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  • 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.