Level lowering on Siegel modular threefold of paramodular level
Number Theory
2022-09-26 v3 Algebraic Geometry
Abstract
In this article we prove several level lowering results for cuspidal automorphic representations occurring in the cohomology of the Siegel modular threefold with paramodular level structure by adapting a method of Ribet in his proof of the Serre's epsilon conjecture. The proof is purely geometric and relies on the description of the supersingular locus of certain quaternionic unitary Shimura variety and an arithmetic level raising result on this Shimura variety. The heart of the proof is a comparison of the dimension of the space of vanishing cycles on the paramodular Siegel modular threefold with that on the quaternionic unitary Shimura variety.
Keywords
Cite
@article{arxiv.1910.07569,
title = {Level lowering on Siegel modular threefold of paramodular level},
author = {Haining Wang},
journal= {arXiv preprint arXiv:1910.07569},
year = {2022}
}
Comments
completely rewrite from the previous version