Vol. 8, No. 9, 2014

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Finiteness of unramified deformation rings

Patrick B. Allen and Frank Calegari

Vol. 8 (2014), No. 9, 2263–2272
Abstract

We prove that the universal unramified deformation ring Runr of a continuous Galois representation ρ̄ : GF+ GLn(k) (for a totally real field F+ and finite field k) is finite over O = W(k) in many cases. We also prove (under similar hypotheses) that the universal deformation ring Runiv is finite over the local deformation ring Rloc.

Keywords
Galois representations
Mathematical Subject Classification 2010
Primary: 11F80
Secondary: 11F70
Milestones
Received: 1 June 2014
Revised: 22 September 2014
Accepted: 12 November 2014
Published: 28 December 2014
Authors
Patrick B. Allen
Mathematics Department
Northwestern University
2033 Sheridan Road
Evanston, IL 60208
United States
Frank Calegari
Department of Mathematics
Northwestern University
2033 Sheridan Road
Evanston, IL 60208
United States