Serre weight conjectures for $\mathrm{GSp}_4$
Number Theory
2025-10-07 v1
Abstract
We prove the weight part of Serre's conjecture for Galois representations valued in that are tamely ramified with explicit genericity at places above as conjectured by Herzig--Tilouine and Gee--Herzig--Savitt. This improves on arXiv:2304.13879 where an inexplicit genericity hypothesis was required. As an application, we prove a modularity lifting theorem for under similar assumptions.
Cite
@article{arxiv.2510.04805,
title = {Serre weight conjectures for $\mathrm{GSp}_4$},
author = {Daniel Le and Bao V. Le Hung and Heejong Lee},
journal= {arXiv preprint arXiv:2510.04805},
year = {2025}
}
Comments
36 pages. Comments are welcome!