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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 $mathbf{Q}$. 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.
Let $F$ be a totally real field in which $p$ is unramified. We prove that, if a cuspidal overconvergent Hilbert cuspidal form has small slopes under $U_p$-operators, then it is classical. Our method follows the original cohomological approach of Cole
We explain how to construct a cohomology theory on the category of separated quasi-compact smooth rigid spaces over $mathbf{C}_p$ (or more general base fields), taking values in the category of vector bundles on the Fargues-Fontaine curve, which exte
Let $F$ be a quadratic real field, $p$ be a rational prime inert in $F$. In this paper, we prove that an overconvergent $p$-adic Hilbert eigenform for $F$ of small slope is actually a classical Hilbert modular form.
Let $Gamma$ be a finitely generated Fuchsian group of the first kind which has at least one parabolic class. Eichler introduced a cohomology theory for Fuchsian groups, called as Eichler cohomology theory, and established the $CC$-linear isomorphism
In this paper we present an algorithm for computing Hecke eigensystems of Hilbert-Siegel cusp forms over real quadratic fields of narrow class number one. We give some illustrative examples using the quadratic field $Q(sqrt{5})$. In those examples, w