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 |
| _version_ | 1826217664191660032 |
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| author | Shankar, Ananth N. Zhou, Rong |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Shankar, Ananth N. Zhou, Rong |
| author_sort | Shankar, Ananth N. |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T17:07:17Z |
| format | Article |
| id | mit-1721.1/132050 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T17:07:17Z |
| publishDate | 2021 |
| publisher | Springer Berlin Heidelberg |
| record_format | dspace |
| spelling | mit-1721.1/1320502023-11-07T20:00:21Z Serre–Tate theory for Shimura varieties of Hodge type Shankar, Ananth N. Zhou, Rong Massachusetts Institute of Technology. Department of Mathematics 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. 2021-09-20T17:41:39Z 2021-09-20T17:41:39Z 2020-07-15 2021-03-13T04:22:44Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/132050 en https://doi.org/10.1007/s00209-020-02556-y Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. Springer-Verlag GmbH Germany, part of Springer Nature application/pdf Springer Berlin Heidelberg Springer Berlin Heidelberg |
| spellingShingle | Shankar, Ananth N. Zhou, Rong Serre–Tate theory for Shimura varieties of Hodge type |
| title | Serre–Tate theory for Shimura varieties of Hodge type |
| title_full | Serre–Tate theory for Shimura varieties of Hodge type |
| title_fullStr | Serre–Tate theory for Shimura varieties of Hodge type |
| title_full_unstemmed | Serre–Tate theory for Shimura varieties of Hodge type |
| title_short | Serre–Tate theory for Shimura varieties of Hodge type |
| title_sort | serre tate theory for shimura varieties of hodge type |
| url | https://hdl.handle.net/1721.1/132050 |
| work_keys_str_mv | AT shankarananthn serretatetheoryforshimuravarietiesofhodgetype AT zhourong serretatetheoryforshimuravarietiesofhodgetype |