Galois Representations for Holomorphic Siegel Modular Forms
نویسنده
چکیده
We prove local global compatibility (up to a quadratic twist) of Galois representations associated to holomorphic Hilbert-Siegel modular forms in many cases (induced from Borel or Klingen parabolic). For Siegel modular forms, when the local representation is an irreducible principal series we get local global compatibility without a twist. We achieve this by proving a version of rigidity (strong multiplicity one) for GSp(4) using, on the one hand the doubling method to compute the standard L-function, and on the other hand the explicit classification of the irreducible local representations of GSp(4); then we refer to [Sor10] for local global compatibility in the case of globally generic Hilbert-Siegel modular forms.
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