p-adic families and Galois representations for GS_p(4) and GL(2)

Creators: Jorza, Andrei

Abstract

In this brief paper, we prove local-global compatibility for holomorphic Siegel modular forms with Iwahori level. In previous work, we proved a weaker version of this result (up to a quadratic twist) and one of the goals of this paper is to remove this quadratic twist by different methods, using p-adic families. We further study the local Galois representation at p for nonregular holomorphic Siegel modular forms. Then we apply the results to the setting of modular forms on GL(2) over a quadratic imaginary field and prove results on the local Galois representation ℓ, as well as crystallinity results at p.

Additional Information

© 2012 International Press of Boston. Received by the editors November 09, 2011. Parts of these notes are based on the authors thesis, written under the supervision of Andrew Wiles. The author is grateful to him and to Christopher Skinner for their help. The author is also grateful to Martin Luu for discussions that led to the removal of the quadratic twists appearing in the author's previous result on local-global compatibility, and to Dinakar Ramakrishnan for many helpful conversations, and for his careful reading of these notes.

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p-adic families and Galois representations for GS_p(4) and GL(2)

Abstract

Additional Information

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