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- W2038432482 abstract "Fix a prime $l$ and let $M$ be an integer such that $lnot|M$. Let $fin S_2(Gamma_1(M l^2))$ be a newform which is supercuspidal at $l$ of a fixed type related to the nebentypus and special at a finite set of primes. Let $mathbf{T}^psi$ be the local quaternionic Hecke algebra associated to $f$. The algebra $mathbf{T}^psi$ acts on a module $mathcal M^psi_f$ coming from the cohomology of a Shimura curve. It follows from the Taylor-Wiles criterion and a recent Savitt's theorem, that $mathbf{T}^psi$ 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 $mathbf{T}^psi$. If $f$ occurs at minimal level, we prove a result about congruences of ideals and we obtain a raising the level result. The extension of these results to the non minimal case is still an open problem." @default.
- W2038432482 created "2016-06-24" @default.
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- W2038432482 date "2009-09-01" @default.
- W2038432482 modified "2023-10-03" @default.
- W2038432482 title "Congruences between modular forms and related modules" @default.
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- W2038432482 doi "https://doi.org/10.7169/facm/1254330159" @default.
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