Algebra & Number Theory

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

Lue Pan

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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.

Article information

Source
Algebra Number Theory, Volume 11, Number 2 (2017), 405-503.

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

Permanent link to this document
https://projecteuclid.org/euclid.ant/1510842738

Digital Object Identifier
doi:10.2140/ant.2017.11.405

Mathematical Reviews number (MathSciNet)
MR3641878

Zentralblatt MATH identifier
06722473

Subjects
Primary: 11S37: Langlands-Weil conjectures, nonabelian class field theory [See also 11Fxx, 22E50]
Secondary: 22E50: Representations of Lie and linear algebraic groups over local fields [See also 20G05] 11F85: $p$-adic theory, local fields [See also 14G20, 22E50] 11G25: Varieties over finite and local fields [See also 14G15, 14G20]

Keywords
Drinfel'd upper half-plane $p$-adic local Langlands correspondence of $\mathrm{GL}_2(\mathbb{Q}_p)$

Citation

Pan, Lue. First covering of the Drinfel'd upper half-plane and Banach representations of $\mathrm{GL}_2(\mathbb{Q}_p)$. Algebra Number Theory 11 (2017), no. 2, 405--503. doi:10.2140/ant.2017.11.405. https://projecteuclid.org/euclid.ant/1510842738


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