Normes invariantes et existence de filtrations admissibles

Details Normes invariantes et existence de filtrations admissibles Normes invariantes et existence de filtrations admissibles

2007-09-19

arxiv.org/abs/0709.3122v2

Crelle's journal, No.634 (2009), Pages 107-141

Mathematics

Number Theory

30 pages

Scientific paper

Let L be a finite extension of Q_p and d a positive integer. A conjecture, due to C. Breuil and P. Schneider, says that the existence of invariant norms on certain locally algebraic representations of GL_{d+1}(L) should be equivalent to the existence of certain (d+1)-dimensional de Rham representations of Gal(\bar{L}/L). We prove the easy direction of this conjecture: the existence of invariant norms implies the existence of admissible filtrations, by generalizing an idea of M.Emerton.

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