On admissible tensor products in $p$-adic Hodge theory

Details On admissible tensor products in $p$-adic Hodge theory On admissible tensor products in $p$-adic Hodge theory

2011-03-11

arxiv.org/abs/1103.2231v4

Mathematics

Number Theory

Scientific paper

We prove that if $W$ and $W'$ are two $B$-pairs whose tensor product is crystalline (or semi-stable or de Rham or Hodge-Tate), then there exists a character $\mu$ such that $W(\mu^{-1})$ and $W'(\mu)$ are crystalline (or semi-stable or de Rham or Hodge-Tate). We also prove that if $W$ is a $B$-pair and $F$ is a Schur functor (for example $\Sym^n(-)$ or $\Lambda^n(-)$) 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 $\mu$ such that $W(\mu^{-1})$ is crystalline (or semi-stable or de Rham or Hodge-Tate). In particular, these results apply to $p$-adic representations.

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