Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.07737 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910298326171648 |
|---|---|
| author | Fornea, Michele Gehrmann, Lennart |
| author_facet | Fornea, Michele Gehrmann, Lennart |
| contents | Plectic Stark-Heegner points were recently introduced to explore the arithmetic of higher rank elliptic curves: the concept was inspired by Nekovář 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_07737 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-Archimedean plectic Jacobians Fornea, Michele Gehrmann, Lennart Number Theory Plectic Stark-Heegner points were recently introduced to explore the arithmetic of higher rank elliptic curves: the concept was inspired by Nekovář 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. |
| title | Non-Archimedean plectic Jacobians |
| topic | Number Theory |
| url | https://arxiv.org/abs/2401.07737 |