The $p$-adic Gross-Zagier formula on Shimura curves, II: nonsplit primes
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2019
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| _version_ | 1866929253133582336 |
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| author | Disegni, Daniel |
| author_facet | Disegni, Daniel |
| contents | The formula of the title relates $p$-adic heights of Heegner points and derivatives of $p$-adic $L$-functions. It was originally proved by Perrin-Riou for $p$-ordinary elliptic curves over the rationals, under the assumption that $p$ splits in the relevant quadratic extension. We remove this assumption, in the more general setting of Hilbert-modular abelian varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1907_13040 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | The $p$-adic Gross-Zagier formula on Shimura curves, II: nonsplit primes Disegni, Daniel Number Theory 11G40, 11F33, 11G50, 11F41 The formula of the title relates $p$-adic heights of Heegner points and derivatives of $p$-adic $L$-functions. It was originally proved by Perrin-Riou for $p$-ordinary elliptic curves over the rationals, under the assumption that $p$ splits in the relevant quadratic extension. We remove this assumption, in the more general setting of Hilbert-modular abelian varieties. |
| title | The $p$-adic Gross-Zagier formula on Shimura curves, II: nonsplit primes |
| topic | Number Theory 11G40, 11F33, 11G50, 11F41 |
| url | https://arxiv.org/abs/1907.13040 |