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Congruences between Hilbert modular forms: constructing ordinary lifts

Congruences between Hilbert modular forms: constructing ordinary lifts

Authors :
Toby Gee
David Geraghty
Thomas Barnet-Lamb
Source :
Duke Math. J. 161, no. 8 (2012), 1521-1580
Publication Year :
2012
Publisher :
Duke University Press, 2012.

Abstract

Under mild hypotheses, we prove that if F is a totally real field, k is the algebraic closure of the finite field with l elements and r : G_F --> GL_2(k) is irreducible and modular, then there is a finite solvable totally real extension F'/F such that r|_{G_F'} has a modular lift which is ordinary at each place dividing l. We deduce a similar result for r itself, under the assumption that at places v|l the representation r|_{G_F_v} 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.<br />48 pages

Details

ISSN :
00127094
Volume :
161
Database :
OpenAIRE
Journal :
Duke Mathematical Journal
Accession number :
edsair.doi.dedup.....6b0d02fdaf079977a968af6676938db5
Full Text :
https://doi.org/10.1215/00127094-1593326