On triangulable tensor products of B-pairs and trianguline representations
We show that if V and V' are two p-adic representations of Gal(Qp^alg/Qp) whose tensor product is trianguline, then V and V' are both potentially trianguline.
math.NT↗
arXiv subjects
Giovanni Di Matteo
Publications and source records attributed to Giovanni Di Matteo.
On admissible tensor products in $p$-adic Hodge theory
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 $μ$ 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 $F$ is a Schur functor (for example $\Sym^n(-)$ or $Λ^n(-)$) 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 $μ$ 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.
math.NT↗