Vol. 11, No. 2, 2017

Download this article
Download this article For screen
For printing
Recent Issues

Volume 13
Issue 8, 1765–1981
Issue 7, 1509–1763
Issue 6, 1243–1507
Issue 5, 995–1242
Issue 4, 749–993
Issue 3, 531–747
Issue 2, 251–530
Issue 1, 1–249

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Subscriptions
Editors' Interests
Submission Guidelines
Submission Form
Editorial Login
Ethics Statement
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
 
Other MSP Journals
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.

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