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arXiv · 2506.02643

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

Hansheng Diao·Giovanni Rosso·Ju-Feng Wu
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Abstract

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 \'etale cohomology with supports.

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Hansheng Diao, Giovanni Rosso, Ju-Feng Wu. 2025-06-03. Overconvergent Eichler-Shimura morphisms for $\mathrm{GSp}_4$. https://arxiv.org/abs/2506.02643

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