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Congruences between Hilbert modular forms: constructing ordinary lifts
Congruences between Hilbert modular forms: constructing ordinary lifts
- 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
- Subjects :
- Pure mathematics
Conjecture
Mathematics - Number Theory
Rank (linear algebra)
business.industry
Mathematics::Number Theory
General Mathematics
High Energy Physics::Phenomenology
010102 general mathematics
Modular form
11F33
Extension (predicate logic)
Congruence relation
Modular design
01 natural sciences
Unitary state
Lift (mathematics)
0103 physical sciences
FOS: Mathematics
Number Theory (math.NT)
010307 mathematical physics
0101 mathematics
business
Mathematics
Subjects
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