The ring of modular forms of degree two in characteristic three

TL;DR

This paper characterizes the structure of the ring of Siegel modular forms of degree 2 specifically in characteristic 3, providing insights into their algebraic properties in this setting.

Contribution

It explicitly determines the structure of the ring of degree 2 Siegel modular forms in characteristic 3, a case not previously fully understood.

Findings

Explicit description of the ring structure in characteristic 3

Identification of generators and relations for the modular forms

Advancement in understanding modular forms in positive characteristic

Abstract

We determine the structure of the ring of Siegel modular forms of degree 2 in characteristic 3.