Theta operators on unitary Shimura varieties

de Shalit, Ehud; Goren, Eyal Z.

doi:10.2140/ant.2019.13.1829

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Theta operators on unitary Shimura varieties

Ehud de Shalit and Eyal Z. Goren

Vol. 13 (2019), No. 8, 1829–1877

DOI: 10.2140/ant.2019.13.1829

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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Keywords

Shimura variety, theta operator, modular form

Mathematical Subject Classification 2010

Primary: 11G18

Secondary: 14G35

Milestones

Received: 1 January 2018

Revised: 9 January 2019

Accepted: 13 June 2019

Published: 9 October 2019

Authors

Ehud de Shalit
Einstein Institute of Mathematics The Hebrew University of Jerusalem Israel

Eyal Z. Goren
Department of Mathematics and Statistics McGill University Montreal Canada

Vol. 13, No. 8, 2019