# Preprints

## On triangulable tensor products of *B*-pairs and trianguline representations

Let *G*_{Qp} denote the absolute Galois group of **Q**_{p}, and let *E*/**Q**_{p} be a finite extension. We show that if *V* and *V'* are non-zero *E*-linear representations of *G*_{Qp} whose tensor product is trianguline, then *V* and *V'* are potentially trianguline. We give an example showing that *V* and *V'* need not be trianguline. This is a joint paper with L. Berger.

# Publications

## 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.

*Compositio Mathematica 149 (2013), no. 3, pp 417--429.* Online, preprint version.