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arXiv · 1612.06456

Serre-Tate theory for Shimura varieties of Hodge type

Ananth N. Shankar·Rong Zhou
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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.

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Ananth N. Shankar, Rong Zhou. 2016-12-19. Serre-Tate theory for Shimura varieties of Hodge type. https://arxiv.org/abs/1612.06456

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