Congruences between modular forms and related modules
Miriam Ciavarella (2006)
Bollettino dell'Unione Matematica Italiana
Similarity:
We fix a prime and let be an integer such that ; let be a newform supercuspidal of fixed type at and special at a finite set of primes. For an indefinite quaternion algebra over , of discriminant dividing the level of , there is a local quaternionic Hecke algebra associated to . The algebra acts on a module coming from the cohomology of a Shimura curve. Applying the Taylor-Wiles criterion and a recent Savitt's theorem, is the universal deformation ring of a global...