A Taylor–Wiles System for Quaternionic Hecke Algebras

Wiley - 2003
Lea Terracini1
1Dipartimento di Matematica, Università di Torino, Turin, Italy

Tóm tắt

Let &ell >3 be a prime. Fix a regular character χ of F&2 × of order ≤ & − 1, and an integer M prime to &. Let f∈S 2(Γ0(M&2)) be a newform which is supercuspidal of type χ at &. For an indefinite quaternion algebra over Q of discriminant dividing the level of f, there is a local quaternionic Hecke algebra T of type χ associated to f. The algebra T acts on a quaternionic cohomological module M. We construct a Taylor–Wiles system for M, and prove that T is the universal object for a deformation problem (of type χ at & and semi-stable outside) of the Galois representation ρ¯ f over F¯& associated to f; that T is complete intersection and that the module M is free of rank 2 over T. We deduce a relation between the quaternionic congruence ideal of type χ for f and the classical one.

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