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Automorphy of some residually S5 Galois representations

Accepted version
Peer-reviewed

Type

Article

Change log

Authors

Khare, Chandrashekhar B 
Thorne, Jack A 

Abstract

Let F be a totally real field and p an odd prime. We prove an automorphy lifting theorem for geometric representations ρ : GF → GL2(Q¯p) which lift irreducible residual representations ρ¯ that arise from Hilbert modular forms. The new result is that we allow the case p = 5, ρ¯ has projective image S5 PGL2(F5) and the fixed field of the kernel of the projective representation contains ζ5. The usual Taylor–Wiles method does not work in this case as there are elements of dual Selmer that cannot be killed by allowing ramification at Taylor–Wiles primes. These elements arise from our hypothesis and the non-vanishing of H1 (PGL2(F5), Ad(1)) where Ad(1) is the adjoint of the natural representation of GL2(F5) twisted by the quadratic character of PGL2(F5).

Description

This is the author accepted manuscript. It is currently under an indefinite embargo pending publication by Springer.

Keywords

4902 Mathematical Physics, 4904 Pure Mathematics, 49 Mathematical Sciences

Journal Title

MATHEMATISCHE ZEITSCHRIFT

Conference Name

Journal ISSN

0025-5874
1432-1823

Volume Title

Publisher

Springer Science and Business Media LLC
Sponsorship
National Science Foundation (Grant ID: DMS-1161671), Humboldt Research Award