The p-adic Gross--Zagier formula on Shimura curves, II: non-split 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 languageEnglish
StatePublished - 2019

Publication series

NameArxiv preprint

Keywords

  • math.NT
  • 11G40, 11F33, 11G50, 11F41

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