Vol. 11, No. 2, 2017

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First covering of the Drinfel'd upper half-plane and Banach representations of $\mathrm{GL}_2(\mathbb{Q}_p)$

Lue Pan

Vol. 11 (2017), No. 2, 405–503
Abstract

For an odd prime p, we construct some admissible Banach representations of GL2(p) that conjecturally should correspond to some 2-dimensional tamely ramified, potentially Barsotti–Tate representations of Gal(p ̄p) via the p-adic local Langlands correspondence. To achieve this, we generalize Breuil’s work in the semistable case and work on the first covering of the Drinfel’d upper half-plane. Our main tool is an explicit semistable model of the first covering.

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Keywords
Drinfel'd upper half-plane, $p$-adic local Langlands correspondence of $\mathrm{GL}_2(\mathbb{Q}_p)$
Mathematical Subject Classification 2010
Primary: 11S37
Secondary: 22E50, 11F85, 11G25
Milestones
Received: 12 October 2015
Revised: 17 June 2016
Accepted: 18 November 2016
Published: 15 April 2017
Authors
Lue Pan
Department of Mathematics
Princeton University
Fine Hall
Washington Road
Princeton, NJ 08540
United States