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Pré-Publication, Document De Travail Année : 2020

$p$-adic families of modular forms for Hodge type Shimura varieties with non-empty ordinary locus

Résumé

We generalize some of the results of Andreatta, Iovita, and Pilloni and the author to Hodge type Shimura varieties having non-empty ordinary locus. For any $p$-adic weight $\kappa$, we give a geometric definition of the space of overconvergent modular forms of weight $\kappa$ in terms of sections of a sheaf. We show that our sheaves live in analytic families, interpolating the classical sheaves for integral weights. We define an action of the Hecke algebra, including a completely continuous operator at $p$. In some simple cases, we also build the eigenvariety.

Dates et versions

hal-04011735 , version 1 (02-03-2023)

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Riccardo Brasca. $p$-adic families of modular forms for Hodge type Shimura varieties with non-empty ordinary locus. 2023. ⟨hal-04011735⟩
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