Heegner cycles and higher weight specializations of big Heegner points

Francesc Castella

Research output: Contribution to journalArticle

8 Scopus citations

Abstract

Let f be a p-ordinary Hida family of tame level N, and let K be an imaginary quadratic field satisfying the Heegner hypothesis relative to N. By taking a compatible sequence of twisted Kummer images of CM points over the tower of modular curves of level Γ0(N) ∩ Γ1(ps), Howard has constructed a canonical class Z in the cohomology of a self-dual twist of the big Galois representation associated to f. If a p-ordinary eigenform f on Γ0(N) of weight k > 2 is the specialization of f at ν, one thus obtains from Zν a higher weight generalization of the Kummer images of Heegner points. In this paper we relate the classes Zν to the étale Abel-Jacobi images of Heegner cycles when p splits in K.

Original languageEnglish (US)
Pages (from-to)1247-1282
Number of pages36
JournalMathematische Annalen
Volume356
Issue number4
DOIs
StatePublished - Aug 1 2013

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Fingerprint Dive into the research topics of 'Heegner cycles and higher weight specializations of big Heegner points'. Together they form a unique fingerprint.

  • Cite this