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Theta operators on unitary Shimura varieties (1712.06969v2)

Published 19 Dec 2017 in math.NT and math.AG

Abstract: We define a theta operator on p-adic vector-valued modular forms on unitary groups of arbitrary signature, over a quadratic imaginary field in which p is inert. We study its effect on Fourier-Jacobi expansions and prove that it extends holomorphically beyond the {\mu}-ordinary locus, when applied to scalar-valued forms.

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