The weight reduction of mod $p$ Siegel modular forms for $GS{p}_4$

Abstract

In this paper we investigate the (classical) weights of mod $p$ Siegel modular forms of degree 2 toward studying Serre's conjecture for $GS{p}_4$. We first construct various theta operators on the space of such forms a la Katz and define the theta cycles for the specific theta operators. Secondly we study the partial Hasse invariants on each Ekedahl-Oort strata and their local behaviors. This enable us to obtain a kind of weight reduction theorem for mod $p$ Siegel modular forms of degree 2 without increasing level.

This is an extended version of my previous article entitled as "The weight in Serre's conjecture for $GS{p}_4$". Lots of revisions have made, in particular, partial Hasse invariants are modified. The proof of Theorem 4.11 is also modified. Accepted from Math Zeitschrift. An online version is comming soon!

References in corpus (2)

• Torsion in the Coherent Cohomology of Shimura Varieties and Galois Representations
• Sections of the Hodge bundle over Ekedahl-Oort strata of Shimura varieties of Hodge type

Cited by in corpus (7)

• Entire theta operators at unramified primes
• On the Bloch-Kato conjecture for the Asai L-function
• Geometric weight-shifting operators on Hilbert modular forms in characteristic p
• Weights of the mod $p$ kernel of the theta operators
• Serre weights for $GS{p}_4$ over totally real fields
• Theta operators on Siegel modular forms and Galois representations
• Differential operators on modular forms (mod p)