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arXiv · 2401.07737

Non-Archimedean plectic Jacobians

Michele Fornea·Lennart Gehrmann
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Abstract

Plectic Stark-Heegner points were recently introduced to explore the arithmetic of higher rank elliptic curves: the concept was inspired by Nekov\'a\v{r} and Scholl's plectic philosophy, while the construction is based on Bertolini and Darmon's groundbreaking use of the $p$-adic uniformization of Shimura curves to study the Birch-Swinnerton-Dyer conjecture. In this note we give a geometric interpretation of plectic Heegner points using the non-Archimedean uniformization of higher-dimensional quaternionic Shimura varieties. To this end, we define and study a plectic Jacobian functor from a category of Mumford varieties to topological groups extending the classical Jacobian functor on Mumford curves.

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Michele Fornea, Lennart Gehrmann. 2024-01-15. Non-Archimedean plectic Jacobians. https://arxiv.org/abs/2401.07737

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