On the exceptional specializations of big heegner points

Francesc Castella

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5 Scopus citations

Abstract

We extend the -adic Gross-Zagier formula of Bertolini et al. [Generalized Heegner cycles and -adic Rankin -series, Duke Math. J. 162(6) (2013), 1033-1148] to the semistable non-crystalline setting, and combine it with our previous work [Castella, On the -adic variation of Heegner points, Preprint, 2014, arXiv:1410.6591] to obtain a derivative formula for the specializations of Howard's big Heegner points [Howard, Variation of Heegner points in Hida families, Invent. Math. 167(1) (2007), 91-128] at exceptional primes in the Hida family.

Original languageEnglish (US)
Pages (from-to)207-240
Number of pages34
JournalJournal of the Institute of Mathematics of Jussieu
Volume17
Issue number1
DOIs
StatePublished - Jan 1 2018

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • Heegner points
  • Hida families
  • L-invariants
  • p-adic L-functions

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