A vanishing theorem for vector-valued Siegel automorphic forms in characteristic $p$

TL;DR

This paper proves that vector-valued Siegel automorphic forms over characteristic p vanish outside a specific weight range, supporting a broader conjecture about Hodge-type Shimura varieties.

Contribution

It establishes a vanishing theorem for vector-valued Siegel automorphic forms in characteristic p, confirming a special case of a conjecture related to Hodge-type Shimura varieties.

Findings

Space of forms is zero outside explicit weight locus

Supports conjecture on Hodge-type Shimura varieties

Advances understanding of automorphic forms in characteristic p

Abstract

We show that the space of vector-valued Siegel automorphic forms in characteristic $p$ is zero when the weight is outside of an explicit locus. This result is a special case of a general conjecture about Hodge-type Shimura varieties formulated in previous work with W. Goldring.