Overconvergent Eichler—Shimura morphisms for Siegel modular forms

Abstract: A theorem of Faltings—Chai provides a comparison between the étale cohomology of the Siegel modular variety and the coherent cohomology of automorphic sheaves, which generalises the classical Eichler—Shimura decomposition in the case of modular forms. In this talk, based on joint work with Hansheng Diao and Giovanni Rosso, I will discuss how to $p$-adically interpolate the result of Faltings—Chai. The strategy is inspired by the work of Chojecki—Hansen—Johansson; one of the key ingredients is Higher Coleman Theory, recently introduced by Boxer—Pilloni.

number theory

Audience: researchers in the topic

London number theory seminar

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For a record of talks predating this website see: wwwf.imperial.ac.uk/~buzzard/LNTS/numbtheo_past.html