Existence de normes invariantes pour GL₂

2012/07/18 by Marco De Ieso, De Ieso, Marco
Mathematics · #11F #11S #20C #20G #22E #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:11F #msc:11S #msc:20C #msc:20G #msc:22E

paper · pdf · doi:10.48550/arxiv.1207.4517

25 pages, in French

arxiv created 2012/07/18 · arxiv updated 2012/07/20

Abstract

Breuil et Schneider formulated a conjecture on the equivalence of the existence of invariant norms on certain locally algebraic representations of GL_d(F) and the existence of certain de Rham representations of Gal((Q_p)/F), where F is a finite extension of Q_p. In this paper we prove that in the case d = 2 and under some conditions, the existence of certains admissible filtrations implies the existence of invariant norms.

Related

• Existence of invariant norms in p-adic representations of GL₂(F) of\n large weights
• A proof of the Breuil-Schneider conjecture in the indecomposable case
• Admissible unitary completions of locally Q_p-rational representations of GL₂(F)
• Space of norms on locally algebraic representations
• L-invariants, partially de Rham families and local-global compatibility