On relative integral monodromy of abelian logarithms and normal functions
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866910782509285376 |
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| author | André, Yves |
| author_facet | André, Yves |
| contents | The relative algebraic monodromy of abelian logarithms (defined as the kernel of a map between algebraic monodromy groups attached to an abelian scheme with and without a section) was computed in \cite{A1}: under natural assumptions, this vector group turns out to be maximal.
The relative integral monodromy of abelian logarithms is defined similarly as a kernel of integral monodromy groups, without taking Zariski closures. We show that if the integral monodromy of the abelian scheme is a lattice in the algebraic monodromy (which is not always the case), then the relative integral monodromy of the abelian logarithm is also a lattice in the relative algebraic monodromy. The proof uses a Hodge-theoretic interpretation of sections of abelian schemes.
We also consider relative integral monodromy groups in the more general context of normal functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_07691 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On relative integral monodromy of abelian logarithms and normal functions André, Yves Algebraic Geometry 11G, 14K The relative algebraic monodromy of abelian logarithms (defined as the kernel of a map between algebraic monodromy groups attached to an abelian scheme with and without a section) was computed in \cite{A1}: under natural assumptions, this vector group turns out to be maximal. The relative integral monodromy of abelian logarithms is defined similarly as a kernel of integral monodromy groups, without taking Zariski closures. We show that if the integral monodromy of the abelian scheme is a lattice in the algebraic monodromy (which is not always the case), then the relative integral monodromy of the abelian logarithm is also a lattice in the relative algebraic monodromy. The proof uses a Hodge-theoretic interpretation of sections of abelian schemes. We also consider relative integral monodromy groups in the more general context of normal functions. |
| title | On relative integral monodromy of abelian logarithms and normal functions |
| topic | Algebraic Geometry 11G, 14K |
| url | https://arxiv.org/abs/2501.07691 |