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arXiv · 1712.06969

Theta operators on unitary Shimura varieties

Ehud De Shalit·Eyal Z. Goren
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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 μ-ordinary locus, when applied to scalar-valued forms.

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Ehud De Shalit, Eyal Z. Goren. 2019-06-14. Theta operators on unitary Shimura varieties. https://doi.org/10.2140/ant.2019.13.1829

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