Hida theory for Shimura varieties of Hodge type

2021/04/24 by Zhang, Xiaoyu
#11F33 #11F55 #11F60 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2104.11941

Abstract

In this article, we generalize the work of H.Hida and V.Pilloni to construct p-adic families of μ-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 ℚ and is unramified at p, such that the adjoint quotient G^ad has no simple factors isomorphic to PGL₂.

Related

• p-adic families of modular forms for Hodge type Shimura varieties with non-empty ordinary locus
• Derived special cycles on Shimura varieties
• Good Reductions of Shimura Varieties of Hodge Type in Arbitrary Unramified Mixed Characteristic, Part II
• The Hodge conjecture and arithmetic quotients of complex balls
• The μ-ordinary locus for Shimura varieties of Hodge type