On some crystalline representations of GL2(ℚp)

Paškūnas, Vytautas

doi:10.2140/ant.2009.3.411

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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

DOI: 10.2140/ant.2009.3.411

Abstract

We show that the universal unitary completion of certain locally algebraic representation of $G : = {GL}_{2} (ℚ_{p})$ 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

Vol. 3, No. 4, 2009