Serre-Tate theory for Shimura varieties of Hodge type
Number Theory
2020-07-29 v2 Algebraic Geometry
Abstract
We study the formal neighbourhood of a point in -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.
Keywords
Cite
@article{arxiv.1612.06456,
title = {Serre-Tate theory for Shimura varieties of Hodge type},
author = {Ananth N. Shankar and Rong Zhou},
journal= {arXiv preprint arXiv:1612.06456},
year = {2020}
}
Comments
Some more details added. Appendix moved to main body of text as section 5