The weight reduction of mod $p$ Siegel modular forms for $GSp_4$

Takuya Yamauchi

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arXiv · 1410.7894

The weight reduction of mod $p$ Siegel modular forms for $GSp_4$

Takuya Yamauchi

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Abstract

In this paper we investigate the (classical) weights of mod $p$ Siegel modular forms of degree 2 toward studying Serre's conjecture for $GSp_4$. 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.

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Takuya Yamauchi. 2014-10-29. The weight reduction of mod $p$ Siegel modular forms for $GSp_4$. https://arxiv.org/abs/1410.7894

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