Serre-Tate theory for Shimura varieties of Hodge type

Abstract

We study the formal neighbourhood of a point in $\mu$-ordinary locus of an integral model of a Hodge type Shimura variety. We show that this formal neighbourhood has a structure of a shifted cascade. Moreover we show that the CM points on the formal neighbourhood are dense and that the identity section of the shifted cascade corresponds to a lift of the abelian variety which has a characterization in terms of its endomorphisms in analogy with the Serre-Tate canonical lift of an ordinary abelian variety.

Some more details added. Appendix moved to main body of text as section 5

References in corpus (1)

• Towards a theory of local Shimura varieties

Cited by in corpus (3)

• On the Hodge-Newton filtration for p-divisible groups of Hodge type
• Eichler-Shimura Relations for Shimura Varieties of Hodge Type
• The Manin-Mumford conjecture and the Tate-Voloch conjecture for a product of Siegel moduli spaces