Hida theory for Shimura varieties of Hodge type


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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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