p-ADIC FAMILIES AND GALOIS REPRESENTATIONS FOR GSp(4) AND GL(2)
نویسنده
چکیده
In this brief article 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 article 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 `, as well as crystallinity results at p.
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