The image of complex conjugation inl-adic representations associated to automorphic forms

The image of complex conjugation in l-adic representations associated to automorphic forms

Automorphic forms and - adic representations 4

In Carayol’s note [4], a geometric construction of the Galois representations associated to Hilbert modular forms and the compatibility with the local Langlands correspondence are discussed. In loc. cit., the compatibility is established in the case = p where the Galois representation is an -adic representation and p is the prime divided by the prime p of the totally real field where the restri...

Automorphic forms and - adic representations 4 Takeshi Saito

In Carayol’s note [4], a geometric construction of the Galois representations associated to Hilbert modular forms and the compatibility with the local Langlands correspondence are discussed. In loc. cit., the compatibility is established in the case = p where the Galois representation is an -adic representation and p is the prime divided by the prime p of the totally real field where the restri...

`-adic Representations Associated to Modular Forms over Imaginary Quadratic Fields

Let π be a regular algebraic cuspidal automorphic representation of GL2 over an imaginary quadratic number field K, and let ` be a prime number. Assuming the central character of π is invariant under the non-trivial automorphism of K, it is shown that there is a continuous irreducible `-adic representation ρ of Gal(K/K) such that L(s, ρv) = L(s, πv) whenever v is a prime of K outside an explici...

Modular Forms and - adic Representations ∗

the circumstance that L-functions can be introduced not only in the context of automorphic forms, with which he has had some experience, but also in the context of diophantine geometry. That this circumstance can be the source of deep problems was, I believe, first perceived by E. Artin. He was, to be sure, concerned with forms on GL(1) and with varieties of dimension 0. This remains the only c...