2025/06/03 by Hansheng Diao, Giovanni Rosso, Diao, Hansheng +3
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Mathematical Analysis and Transform Methods
paper · pdf · doi:10.48550/arxiv.2506.02643
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 H0-part. The key new inputs are the higher Coleman theory of Boxer-Pilloni and a theory of pro-Kummer étale cohomology with supports.