Représentations potentiellement triangulines de dimension 2

2009/05/24 by Laurent Berger, Berger, Laurent, Gaëtan Chenevier +1
Mathematics · #11F33 #11F80 #11F85 #11S15 #11S20 #11S25 #14D15 #14F30 #14G22 #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT) #math.NT #math.RT #msc:11F33 #msc:11F80 #msc:11F85 #msc:11S15 #msc:11S20 #msc:11S25 #msc:14D15 #msc:14F30 #msc:14G22

paper · pdf · doi:10.48550/arxiv.0905.3880

18 pages; French; English abstract

arxiv created 2009/12/17 · arxiv updated 2010/01/07

Abstract

The two main results of this note are on the one hand that if V is a 2-dimensional potentially trianguline representation of G_Qp then V satisfies at least one of the following properties (1) V is split trianguline (2) V is a direct sum of characters or an induced representation (3) V is a twist of a de Rham representation, and on the other hand that there exists some 2-dimensional representations of G_Qp which are not potentially trianguline.

Related

• Non-regular trianguline representations
• On triangulable tensor products of B-pairs and trianguline\n representations
• Modularity of trianguline Galois representations
• On some partially de Rham Galois representations
• Lifting trianguline Galois representations along isogenies