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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.19476 |
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Table of Contents:
- Let's fix a complex abelian scheme $\mathcal A\to S$ of relative dimension $g$, without fixed part, and having maximal variation in moduli. We show that the relative monodromy group $M^{\textrm{rel}}_σ$ of a ramified section $σ\colon S\to\mathcal A$ is nontrivial. Moreover, under some hypotheses on the action of the monodromy group $\textrm{Mon}(\mathcal A)$ we show that $M^{\textrm{rel}}_σ\cong \mathbb Z^{2g}$. We discuss several examples and applications. For instance we provide a new proof of Manin's kernel theorem and of the algebraic independence of the coordinates of abelian logarithms with respect to the coordinates of periods.