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- W2950082098 abstract "We fix $ell$ a prime and let $M$ be an integer such that $ellnot|M$; let $fin S_2(Gamma_1(Mell^2))$ be a newform supercuspidal of fixed type related to the nebentypus, at $ell$ and special at a finite set of primes. Let $TT^psi$ be the local quaternionic Hecke algebra associated to $f$. The algebra $TT^psi$ acts on a module $mathcal M^psi_f$ coming from the cohomology of a Shimura curve. Applying the Taylor-Wiles criterion and a recent Savitt's theorem, $TT^psi$ is the universal deformation ring of a global Galois deformation problem associated to $orho_f$. Moreover $mathcal M^psi_f$ is free of rank 2 over $TT^psi$. If $f$ occurs at minimal level, by a generalization of a Conrad, Diamond and Taylor's result and by the classical Ihara's lemma, we prove a theorem of raising the level and a result about congruence ideals. The extension of this results to the non minimal case is an open problem." @default.
- W2950082098 created "2019-06-27" @default.
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- W2950082098 date "2007-10-25" @default.
- W2950082098 modified "2023-09-27" @default.
- W2950082098 title "Congruences between modular forms and related modules" @default.
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