On the-Adic variation of heegner points

Francesc Castella

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


In this paper, we prove an 'explicit reciprocity law' relating Howard's system of big Heegner points to a two-variable-Adic-function (constructed here) interpolating the-Adic Rankin-series of Bertolini-Darmon-Prasanna in Hida families. As applications, we obtain a direct relation between classical Heegner cycles and the higher weight specializations of big Heegner points, refining earlier work of the author, and prove the vanishing of Selmer groups of CM elliptic curves twisted by 2-dimensional Artin representations in cases predicted by the equivariant Birch and Swinnerton-Dyer conjecture.

Original languageEnglish (US)
Pages (from-to)2127-2164
Number of pages38
JournalJournal of the Institute of Mathematics of Jussieu
Issue number6
StatePublished - Nov 1 2020
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Mathematics


  • 2010 Mathematics subject classification: 11G05 11G40


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