On Special Subvarieties of the Universal Semi-abelian Scheme and Pink Conjectures
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929557908488192 |
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| author | Gu, Kaiyuan Huang, Chenxin |
| author_facet | Gu, Kaiyuan Huang, Chenxin |
| contents | The universal Poincaré torsor, or more generally the universal semi-abelian scheme, can be viewed as a mixed Shimura variety. We give a classification of special subvarieties of the universal semi-abelian scheme of arbitrary toric rank.
Given this classification, we show that the Zilber-Pink conjecture for mixed Shimura varieties implies the Zilber-Pink conjecture for semi-abelian varieties, correcting an error in an unpublished manuscript of Pink. Moreover, we give a more reasonable reformulation of the Relative Manin-Mumford Conjecture for semi-abelian schemes. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_17755 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Special Subvarieties of the Universal Semi-abelian Scheme and Pink Conjectures Gu, Kaiyuan Huang, Chenxin Algebraic Geometry Number Theory 14K05, 14G35, 11G15 The universal Poincaré torsor, or more generally the universal semi-abelian scheme, can be viewed as a mixed Shimura variety. We give a classification of special subvarieties of the universal semi-abelian scheme of arbitrary toric rank. Given this classification, we show that the Zilber-Pink conjecture for mixed Shimura varieties implies the Zilber-Pink conjecture for semi-abelian varieties, correcting an error in an unpublished manuscript of Pink. Moreover, we give a more reasonable reformulation of the Relative Manin-Mumford Conjecture for semi-abelian schemes. |
| title | On Special Subvarieties of the Universal Semi-abelian Scheme and Pink Conjectures |
| topic | Algebraic Geometry Number Theory 14K05, 14G35, 11G15 |
| url | https://arxiv.org/abs/2410.17755 |