Hida theory for Shimura varieties of Hodge type

Xiaoyu Zhang

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arXiv · 2104.11941

Hida theory for Shimura varieties of Hodge type

Xiaoyu Zhang

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Abstract

In this article, we generalize the work of H.Hida and V.Pilloni to construct $p$-adic families of $\mu$-ordinary modular forms on Shimura varieties of Hodge type $Sh(G,X)$ associated to a Shimura datum $(G,X)$ where $G$ is a connected reductive group over $\mathbb{Q}$ and is unramified at $p$, such that the adjoint quotient $G^\mathrm{ad}$ has no simple factors isomorphic to $\mathrm{PGL}_2$.

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Xiaoyu Zhang. 2021-04-24. Hida theory for Shimura varieties of Hodge type. https://arxiv.org/abs/2104.11941

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