Vol. 6, No. 7, 2012

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

Volume 18
Issue 5, 847–1038
Issue 4, 631–846
Issue 3, 409–629
Issue 2, 209–408
Issue 1, 1–208

Volume 17, 12 issues

Volume 16, 10 issues

Volume 15, 10 issues

Volume 14, 10 issues

Volume 13, 10 issues

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
Editors’ Interests
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
Other MSP Journals
Crystalline extensions and the weight part of Serre's conjecture

Toby Gee, Tong Liu and David Savitt

Vol. 6 (2012), No. 7, 1537–1559

Let p > 2 be prime. We complete the proof of the weight part of Serre’s conjecture for rank-two unitary groups for mod p representations in the totally ramified case by proving that any Serre weight which occurs is a predicted weight. This completes the analysis begun by Barnet-Lamb, Gee, and Geraghty, who proved that all predicted Serre weights occur. Our methods are a mixture of local and global techniques, and in the course of the proof we use global techniques (as well as local arguments) to establish some purely local results on crystalline extension classes. We also apply these local results to prove similar theorems for the weight part of Serre’s conjecture for Hilbert modular forms in the totally ramified case.

Serre's conjecture, p-adic Hodge theory, automorphy lifting theorems
Mathematical Subject Classification 2010
Primary: 11F33
Received: 2 July 2011
Revised: 4 October 2011
Accepted: 2 November 2011
Published: 4 December 2012
Toby Gee
Imperial College London
United Kingdom
Tong Liu
Department of Mathematics
Purdue University
150 N. University Street
West Lafayette, IN 47907
United States
David Savitt
Department of Mathematics
University of Arizona
617 N. Santa Rita Ave.
PO Box 210089
Tucson, AZ 85721-0089
United States