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Abstract
In [Breuil et Schneider, J. reine angew. Math. 610: 149–180, 2007] is formulated a conjecture on the equivalence of the existence of invariant norms on certain locally algebraic representations of GLd+1(L) and the existence of certain de Rham representations of Gal(
/L), where L is a finite extension of ℚp. In this paper, we prove the “easy” direction of the conjecture: the existence of invariant norms implies the existence of admissible filtrations.
Received: 2007-09-19
Revised: 2008-05-09
Published Online: 2009-07-06
Published in Print: 2009-September
© Walter de Gruyter Berlin · New York 2009