A refined non-vanishing of the $p$-adic logarithm of a rational point on an abelian variety
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866913109199814656 |
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| author | Burungale, Ashay Skinner, Christopher Wan, Xin |
| author_facet | Burungale, Ashay Skinner, Christopher Wan, Xin |
| contents | Inspired by a beautiful formula of Bertolini, Darmon, and Prasanna -- the oft-termed BDP formula -- we address questions about the non-vanishing of non-torsion points under $p$-adic logarithms of abelian varieties. We largely consider situations most applicable to ${\mathrm GL}_2$-type abelian varieties associated with Hilbert modular newforms and Heegner points. Not surprisingly, the main tool employed is the $p$-adic analytic subgroup theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_20886 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A refined non-vanishing of the $p$-adic logarithm of a rational point on an abelian variety Burungale, Ashay Skinner, Christopher Wan, Xin Number Theory Inspired by a beautiful formula of Bertolini, Darmon, and Prasanna -- the oft-termed BDP formula -- we address questions about the non-vanishing of non-torsion points under $p$-adic logarithms of abelian varieties. We largely consider situations most applicable to ${\mathrm GL}_2$-type abelian varieties associated with Hilbert modular newforms and Heegner points. Not surprisingly, the main tool employed is the $p$-adic analytic subgroup theorem. |
| title | A refined non-vanishing of the $p$-adic logarithm of a rational point on an abelian variety |
| topic | Number Theory |
| url | https://arxiv.org/abs/2603.20886 |