#### Vol. 13, No. 8, 2019

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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 $\mu$-ordinary locus, when applied to scalar-valued forms.

##### Keywords
Shimura variety, theta operator, modular form
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