Duke Mathematical Journal

Congruences between Hilbert modular forms: constructing ordinary lifts

Thomas Barnet-Lamb, Toby Gee, and David Geraghty

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Under mild hypotheses, we prove that if F is a totally real field, and ρ¯:GFGL2F¯l is irreducible and modular, then there is a finite solvable totally real extension F/F such that ρ¯GF has a modular lift which is ordinary at each place dividing l. We deduce a similar result for ρ¯ itself, under the assumption that at places v|l the representation ρ¯GFv is reducible. This allows us to deduce improvements to results in the literature on modularity lifting theorems for potentially Barsotti–Tate representations and the Buzzard–Diamond–Jarvis conjecture. The proof makes use of a novel lifting technique, going via rank 4 unitary groups.

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Duke Math. J., Volume 161, Number 8 (2012), 1521-1580.

First available in Project Euclid: 22 May 2012

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Zentralblatt MATH identifier

Primary: 11F33: Congruences for modular and $p$-adic modular forms [See also 14G20, 22E50]


Barnet-Lamb, Thomas; Gee, Toby; Geraghty, David. Congruences between Hilbert modular forms: constructing ordinary lifts. Duke Math. J. 161 (2012), no. 8, 1521--1580. doi:10.1215/00127094-1593326. https://projecteuclid.org/euclid.dmj/1337690407

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