CONGRUENCES BETWEEN HILBERT MODULAR FORMS: CONSTRUCTING ORDINARY LIFTS
CONGRUENCES BETWEEN HILBERT MODULAR FORMS: CONSTRUCTING ORDINARY LIFTS
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DOI：
10.1215/00127094-1593326
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发表时间：
2012-06-01
影响因子：
2.5
通讯作者：
Geraghty, David
中科院分区：
文献类型：
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作者：
Barnet-Lamb, Thomas;Gee, Toby;Geraghty, David
温和的假设下,我们证明,如果F是一个完全真实的领域,和(ρ)栏:G (F) - > GL (2) ((F)栏(l))是不可约和模块化,然后是一个有限的可解的完全真实扩展F ' / F这样(ρ)酒吧反斜杠G (F)有一个模块化的提升普通在每个地方分裂l。我们演绎一个相似的结果(ρ)酒吧本身,在地方的假设下upsilon反斜杠l(ρ)/酒吧反斜杠表示G (F upsilon)是可约。这使我们能够推导出对潜在Barsotti-Tate表示和Buzzard-Diamond-Jarvis猜想的模块化提升定理的文献结果的改进。证明使用了一种新颖的提升技术，通过4阶酉群。
Under mild hypotheses, we prove that if F is a totally real field, and (rho) over bar : G (F) -> GL(2)((F) over bar (l)) is irreducible and modular, then there is a finite solvable totally real extension F' / F such that (rho) over bar backslash G (F') has a modular lift which is ordinary at each place dividing l. We deduce a similar result for (rho) over bar itself, under the assumption that at places upsilon backslash l the representation (rho) over bar backslash G (F upsilon) 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.