Serre–Tate theory for Shimura varieties of Hodge type
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209_2020_2556_ReferencePDF.pdf
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Author(s)
Shankar, Ananth N.
Zhou, Rong
Date Issued
July 15, 2020
Publisher
Springer Berlin Heidelberg
Version
Author's final manuscript
Abstract
Abstract
We study the formal neighbourhood of a point in the
$$\mu $$
μ
-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, analogous to the Serre–Tate canonical lift of an ordinary abelian variety.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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DOI of Published Version
https://doi.org/10.1007/s00209-020-02556-y
