Connected monodromy fields of Jacobians with complex multiplication
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911229566517248 |
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| author | Gallese, Andrea Lombardo, Davide |
| author_facet | Gallese, Andrea Lombardo, Davide |
| contents | We describe an algorithm to compute the minimal field of definition of the Tate classes on powers of a Jacobian $J$ with potential complex multiplication. This field arises as a natural invariant of the Galois representations attached to $J$. We also give closed formulas expressing the periods of anti-holomorphic differential forms on $J$ in terms of the periods of the holomorphic ones. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_21247 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Connected monodromy fields of Jacobians with complex multiplication Gallese, Andrea Lombardo, Davide Number Theory Algebraic Geometry Primary: 11F80, Secondary: 11G15, 14C30, 11Y40, 14K20 We describe an algorithm to compute the minimal field of definition of the Tate classes on powers of a Jacobian $J$ with potential complex multiplication. This field arises as a natural invariant of the Galois representations attached to $J$. We also give closed formulas expressing the periods of anti-holomorphic differential forms on $J$ in terms of the periods of the holomorphic ones. |
| title | Connected monodromy fields of Jacobians with complex multiplication |
| topic | Number Theory Algebraic Geometry Primary: 11F80, Secondary: 11G15, 14C30, 11Y40, 14K20 |
| url | https://arxiv.org/abs/2510.21247 |