Perfectoid overconvergent Siegel modular forms and the overconvergent Eichler-Shimura morphism

2021/05/31 by Diao, Hansheng, Rosso, Giovanni, Wu, Ju-Feng · 1 citation
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2106.00094

Abstract

The aim of this paper is twofold. We first present a construction of overconvergent automorphic sheaves for Siegel modular forms by generalising the perfectoid method, originally introduced by Chojecki-Hansen-Johansson for automorphic forms on compact Shimura curves over Q. These sheaves are then verified to be isomorphic to the ones introduced by Andreatta-Iovita-Pilloni. Secondly, we establish an overconvergent Eichler-Shimura morphism for Siegel modular forms, generalising the result of Andreatta-Iovita-Stevens for elliptic modular forms.

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