Plectic Jacobians

Michele Fornea

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arXiv · 2305.01130

Plectic Jacobians

Michele Fornea

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Abstract

Looking for a geometric framework to study plectic Heegner points, we define a collection of abelian varieties - called plectic Jacobians - using the middle degree cohomology of quaternionic Shimura varieties (QSVs). The construction is inspired by the definition of Griffiths' intermediate Jacobians and rests on Nekovar-Scholl's notion of plectic Hodge structures. Moreover, we construct exotic Abel-Jacobi maps sending certain zero-cycles on QSVs to plectic Jacobians.

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Michele Fornea. 2023-05-02. Plectic Jacobians. https://arxiv.org/abs/2305.01130

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