The relatively perfect Greenberg transform and cycle class maps
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866916371977207808 |
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| author | Bertapelle, Alessandra Suzuki, Takashi |
| author_facet | Bertapelle, Alessandra Suzuki, Takashi |
| contents | Given a scheme over a complete discrete valuation ring of mixed characteristic with perfect residue field, the Greenberg transform produces a new scheme over the residue field thicker than the special fiber. In this paper, we will generalize this transform to the case of imperfect residue field. We will then construct a certain kind of cycle class map defined on this generalized Greenberg transform applied to the Néron model of a semi-abelian variety, which takes values in the relatively perfect nearby cycle functor defined by Kato and the second author. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2009_05084 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | The relatively perfect Greenberg transform and cycle class maps Bertapelle, Alessandra Suzuki, Takashi Number Theory Algebraic Geometry Primary: 11G25. Secondary: 14G20, 14F30 Given a scheme over a complete discrete valuation ring of mixed characteristic with perfect residue field, the Greenberg transform produces a new scheme over the residue field thicker than the special fiber. In this paper, we will generalize this transform to the case of imperfect residue field. We will then construct a certain kind of cycle class map defined on this generalized Greenberg transform applied to the Néron model of a semi-abelian variety, which takes values in the relatively perfect nearby cycle functor defined by Kato and the second author. |
| title | The relatively perfect Greenberg transform and cycle class maps |
| topic | Number Theory Algebraic Geometry Primary: 11G25. Secondary: 14G20, 14F30 |
| url | https://arxiv.org/abs/2009.05084 |