A note on the -adic Galois representations attached to Hilbert modular forms.
Skinner, Christopher (2009)
Documenta Mathematica
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Displaying similar documents to “On -adic geometric representations of .”
A note on the -adic Galois representations attached to Hilbert modular forms.
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This paper is essentially the text of the author’s lecture at the 2001 Journées Arithmétiques. It addresses the problem of identifying in Galois-theoretic terms those two-dimensional, -adic Galois representations associated to holomorphic Hilbert modular newforms.
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We explore the question of how big the image of a Galois representation attached to a -adic modular form with no complex multiplication is and show that for a “generic” set of -adic modular forms (normalized, ordinary eigenforms with no complex multiplication), all have a large image.