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2017 First covering of the Drinfel'd upper half-plane and Banach representations of $\mathrm{GL}_2(\mathbb{Q}_p)$
Lue Pan
Algebra Number Theory 11(2): 405-503 (2017). DOI: 10.2140/ant.2017.11.405

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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Lue Pan. "First covering of the Drinfel'd upper half-plane and Banach representations of $\mathrm{GL}_2(\mathbb{Q}_p)$." Algebra Number Theory 11 (2) 405 - 503, 2017. https://doi.org/10.2140/ant.2017.11.405

Information

Received: 12 October 2015; Revised: 17 June 2016; Accepted: 18 November 2016; Published: 2017
First available in Project Euclid: 16 November 2017

zbMATH: 06722473
MathSciNet: MR3641878
Digital Object Identifier: 10.2140/ant.2017.11.405

Subjects:
Primary: 11S37
Secondary: 11F85, 11G25, 22E50

Rights: Copyright © 2017 Mathematical Sciences Publishers

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Vol.11 • No. 2 • 2017
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