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arXiv · 2510.21247

Connected monodromy fields of Jacobians with complex multiplication

Andrea Gallese·Davide Lombardo
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Abstract

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.

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Andrea Gallese, Davide Lombardo. 2025-10-24. Connected monodromy fields of Jacobians with complex multiplication. https://arxiv.org/abs/2510.21247

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