Vol. 3, No. 4, 2009

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On some crystalline representations of GL$_{\mathsf 2}(\mathbb{Q}_{\mathsf p})$

Vytautas Paškūnas

Vol. 3 (2009), No. 4, 411–421
Abstract

We show that the universal unitary completion of certain locally algebraic representation of G := GL2(p) with p > 2 is nonzero, topologically irreducible, admissible and corresponds to a 2-dimensional crystalline representation with nonsemisimple Frobenius via the p-adic Langlands correspondence for G.

Keywords
p-adic Langlands, universal completion, unitary Banach space representation
Mathematical Subject Classification 2000
Primary: 22E50
Secondary: 11S37, 11S20
Milestones
Received: 7 May 2008
Revised: 9 February 2009
Accepted: 12 March 2009
Published: 15 June 2009
Authors
Vytautas Paškūnas
Universität Bielefeld
Fakultät für Mathematik
Postfach 100131
D-33501 Bielefeld
Germany