Serre–Tate theory for Shimura varieties of Hodge type
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....
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Springer Berlin Heidelberg
2021
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| Online Access: | https://hdl.handle.net/1721.1/132050 |
| Summary: | 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. |
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