Overconvergent Eichler-Shimura morphisms for $\mathrm{GSp}_4$

Fuente: arXiv
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Main Authors: Diao, Hansheng, Rosso, Giovanni, Wu, Ju-Feng
Format: Preprint
Published: 2025
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author Diao, Hansheng
Rosso, Giovanni
Wu, Ju-Feng
author_facet Diao, Hansheng
Rosso, Giovanni
Wu, Ju-Feng
contents We construct explicit Eichler-Shimura morphisms for families of overconvergent Siegel modular forms of genus two. These can be viewed as $p$-adic interpolations of the Eichler-Shimura decomposition of Faltings-Chai for classical Siegel modular forms. In particular, we are able to $p$-adically interpolate the entire decomposition, extending our previous work on the $H^0$-part. The key new inputs are the higher Coleman theory of Boxer-Pilloni and a theory of pro-Kummer étale cohomology with supports.
format Preprint
id arxiv_https___arxiv_org_abs_2506_02643
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Overconvergent Eichler-Shimura morphisms for $\mathrm{GSp}_4$
Diao, Hansheng
Rosso, Giovanni
Wu, Ju-Feng
Number Theory
Algebraic Geometry
We construct explicit Eichler-Shimura morphisms for families of overconvergent Siegel modular forms of genus two. These can be viewed as $p$-adic interpolations of the Eichler-Shimura decomposition of Faltings-Chai for classical Siegel modular forms. In particular, we are able to $p$-adically interpolate the entire decomposition, extending our previous work on the $H^0$-part. The key new inputs are the higher Coleman theory of Boxer-Pilloni and a theory of pro-Kummer étale cohomology with supports.
title Overconvergent Eichler-Shimura morphisms for $\mathrm{GSp}_4$
topic Number Theory
Algebraic Geometry
url https://arxiv.org/abs/2506.02643