A new theta cycle for $GSp_4$ and an Edixhoven type theorem

TL;DR

This paper develops a new theta cycle for GSp_4 over the rationals using modified theta operators that work in all characteristics and weights, leading to an Edixhoven type theorem.

Contribution

It introduces a novel theta cycle for GSp_4 and extends theta operators to all characteristics and weights, enabling new applications.

Findings

Constructed a new theta cycle for GSp_4.

Modified theta operators to work in all characteristics.

Proved an Edixhoven type theorem for GSp_4.

Abstract

In this paper, we investigate a new theta cycle for $GSp_4/\mathbb{Q}$ by using author's theta operators defined in the previous work. In the course of the construction, we also modify the theta operators so that they work in any characteristic, including $p = 2$, and for any weight. As an application, we discuss an Edixhoven type theorem for $GSp_4/\mathbb{Q}$.