Overconvergent Eichler-Shimura morphisms for $\mathrm{GSp}_4$
Number Theory
2025-06-04 v1 Algebraic Geometry
Abstract
We construct explicit Eichler-Shimura morphisms for families of overconvergent Siegel modular forms of genus two. These can be viewed as -adic interpolations of the Eichler-Shimura decomposition of Faltings-Chai for classical Siegel modular forms. In particular, we are able to -adically interpolate the entire decomposition, extending our previous work on the -part. The key new inputs are the higher Coleman theory of Boxer-Pilloni and a theory of pro-Kummer \'etale cohomology with supports.
Cite
@article{arxiv.2506.02643,
title = {Overconvergent Eichler-Shimura morphisms for $\mathrm{GSp}_4$},
author = {Hansheng Diao and Giovanni Rosso and Ju-Feng Wu},
journal= {arXiv preprint arXiv:2506.02643},
year = {2025}
}