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

In this paper we investigate the (classical) weights of mod p Siegel modular forms of degree 2 toward studying Serre’s conjecture for G S p 4 / 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. [ABSTRACT FROM AUTHOR]