Nearly overconvergent Siegel modular forms

Liu, Zheng

Annales de l'Institut Fourier, Tome 69 (2019) no. 6, pp. 2439-2506.

Nous introduisons une formulation faisceau-théorique de la théorie de Shimura des formes modulaires de Siegel quasi holomorphes et des opérateurs différentiels. Nous l’utilisons pour définir et étudier les formes modulaires de Siegel quasi surconvergentes et leurs familles p-adiques

We introduce a sheaf-theoretic formulation of Shimura’s theory of nearly holomorphic Siegel modular forms and differential operators. We use it to define and study nearly overconvergent Siegel modular forms and their $p$-adic families.

Classification : 11F46, 11F33, 11F60, 14J15
Keywords: nearly holomorphic Siegel modular forms, nearly overconvergent Siegel modular forms, differential operators, overconvergent families
Mot clés : formes modulaires de Siegel quasi holomorphes, formes modulaires de Siegel quasi surconvergentes, opérateurs différentiels, familles surconvergentes

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