ON l-ADIC FAMILIES OF CUSPIDAL REPRESENTATIONS OF GL2(Qp)
نویسنده
چکیده
We compute the universal deformations of cuspidal representations π of GL2(F ) over Fl, where F is a local field of residue characteristic p and l is an odd prime different from p. When π is supercuspidal there is an irreducible, two dimensional representation ρ of GF that corresponds to π via the mod l local Langlands correspondence of [Vi2]; we show that there is a natural isomorphism between the universal deformation rings of ρ and π that induces the usual (suitably normalized) local Langlands correspondence on characteristic zero points. Our work establishes certain cases of a conjecture
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