Publications

On triangulable tensor products of B-pairs and trianguline representations

Let G_{Q_p} 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_{Q_p} 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.

Int. J. Number Theory 17 (2021), no. 10, pp. 2221 -- 2233. Journal version, preprint version.

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 Symⁿ(-) 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.

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