Hida theory for Shimura varieties of Hodge type

TL;DR

This paper extends Hida theory to construct $p$-adic families of $$-ordinary modular forms on Shimura varieties of Hodge type, broadening the scope of $p$-adic modular form theory.

Contribution

It generalizes previous work by Hida and Pilloni to a wider class of Shimura varieties of Hodge type, excluding certain simple factors.

Findings

Construction of $p$-adic families of modular forms on Hodge type Shimura varieties.

Extension of Hida theory to new geometric contexts.

Framework for future research in $p$-adic automorphic forms.

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 $\mathrm{PGL}_2$.