## Abstract

We give a new proof of Howard's Λ-adic Gross-Zagier formula Compos. Math. 141 (2005) 811-846. MR 2148200 (2006f:11074)], which we extend to the context of indefinite Shimura curves over Q attached to nonsplit quaternion algebras. This formula relates the cyclotomic derivative of a two-variable p-adic L-function restricted to the anticyclotomic line to the cyclotomic p-adic heights of Heegner points over the anticyclotomic tower, and our proof, rather than inspired by the influential approaches of Gross-Zagier [Invent. Math. 84 (1986) 225-320. MR 833192 (87j:11057)] and Perrin-Riou [Invent. Math. 89 (1987) 455-510. MR 903381 (89d:11034)], is via Iwasawa theory, based on the connection between Heegner points, Beilinson-Flach elements, and their explicit reciprocity laws.

Original language | English (US) |
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Pages (from-to) | 156-180 |

Number of pages | 25 |

Journal | Journal of the London Mathematical Society |

Volume | 96 |

Issue number | 1 |

DOIs | |

State | Published - Aug 2017 |

## All Science Journal Classification (ASJC) codes

- General Mathematics