The weight reduction of mod p Siegel modular forms for GSp4 and theta operators

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper we investigate the (classical) weights of mod p Siegel modular forms of degree 2 toward studying Serre’s conjecture for GSp4/ Q. We first construct various theta operators on the space of such forms à la Katz and define the theta cycles for the specific theta operators. Secondly, we study the partial Hasse invariants on each Ekedahl–Oort stratum and their local behaviors. This enables us to obtain a kind of weight reduction theorem for mod p Siegel modular forms of degree 2 without increasing the level.

Original languageEnglish
Article number10
JournalMathematische Zeitschrift
Volume303
Issue number1
DOIs
Publication statusPublished - 2023 Jan

Keywords

  • Galois representations
  • Mod p Siegel modular forms
  • Partial Hasse invariants

Fingerprint

Dive into the research topics of 'The weight reduction of mod p Siegel modular forms for GSp4 and theta operators'. Together they form a unique fingerprint.

Cite this