The P-Adic Gross-Zagier Formula on Shimura Curves, Ii: Nonsplit Primes

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Abstract

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.

Original languageAmerican English
Pages (from-to)2199-2240
Number of pages42
JournalJournal of the Institute of Mathematics of Jussieu
Volume22
Issue number5
DOIs
StatePublished - 15 Sep 2023

Keywords

  • Heegner points
  • p-adic L-functions
  • p-adic heights

All Science Journal Classification (ASJC) codes

  • General Mathematics

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