The weight reduction of mod $p$ Siegel modular forms for $GSp_4$
Abstract
In this paper we investigate the (classical) weights of mod Siegel modular forms of degree 2 toward studying Serre's conjecture for . 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 Siegel modular forms of degree 2 without increasing level.
Keywords
Cite
@article{arxiv.1410.7894,
title = {The weight reduction of mod $p$ Siegel modular forms for $GSp_4$},
author = {Takuya Yamauchi},
journal= {arXiv preprint arXiv:1410.7894},
year = {2022}
}
Comments
This is an extended version of my previous article entitled as "The weight in Serre's conjecture for $ GSp_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!