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arXiv · 2410.17755

On Special Subvarieties of the Universal Semi-abelian Scheme and Pink Conjectures

Kaiyuan Gu·Chenxin Huang
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Abstract

The universal Poincar\'e 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for mixed Shimura varieties implies the Zilber-Pink conjecture for semi-abelian varieties, correcting an error in an unpublished manuscript of Pink.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.

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Kaiyuan Gu, Chenxin Huang. 2024-10-23. On Special Subvarieties of the Universal Semi-abelian Scheme and Pink Conjectures. https://arxiv.org/abs/2410.17755

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