On the Modularity of Wildly Ramified Galois Representations
نویسنده
چکیده
where GQ = Gal ( Q/Q ) is the absolute Galois group of Q and ` is a fixed rational prime. For example, ρ = ρE,` may be the `-adic representation of an elliptic curve E over Q, or ρ = ρf may be the `-adic representation associated to a modular form. The continuity of such Galois representations implies the image lies in GL2(O) for some ring of integers O with maximal ideal λ in a finite extension K of Q`; then k = O/λ is a finite extension of F`. We define the residual representation ρ as the composition ρ : GQ → GL2 (O)→ GL2 ( F` ) .
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تاریخ انتشار 2003