ON THE NON-TRIVIALITY OF THE -ADIC ABEL–JACOBI IMAGE OF GENERALISED HEEGNER CYCLES MODULO , II: SHIMURA CURVES
Generalised Heegner cycles are associated to a pair of an elliptic newform and a Hecke character over an imaginary quadratic extension $K/\mathbf{Q}$ . The cycles live in a middle-dimensional Chow group of a Kuga–Sato variety arising from an indefinite Shimura curve over the rationals and a self-pro...
Gespeichert in:
Veröffentlicht in: | Journal of the Institute of Mathematics of Jussieu 2017-02, Vol.16 (1), p.189-222 |
---|---|
1. Verfasser: | |
Format: | Artikel |
Sprache: | eng |
Schlagworte: | |
Online-Zugang: | Volltext |
Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
Zusammenfassung: | Generalised Heegner cycles are associated to a pair of an elliptic newform and a Hecke character over an imaginary quadratic extension
$K/\mathbf{Q}$
. The cycles live in a middle-dimensional Chow group of a Kuga–Sato variety arising from an indefinite Shimura curve over the rationals and a self-product of a CM abelian surface. Let
$p$
be an odd prime split in
$K/\mathbf{Q}$
. We prove the non-triviality of the
$p$
-adic Abel–Jacobi image of generalised Heegner cycles modulo
$p$
over the
$\mathbf{Z}_{p}$
-anticyclotomic extension of
$K$
. The result implies the non-triviality of the generalised Heegner cycles in the top graded piece of the coniveau filtration on the Chow group, and proves a higher weight analogue of Mazur’s conjecture. In the case of weight 2, the result provides a refinement of the results of Cornut–Vatsal and Aflalo–Nekovář on the non-triviality of Heegner points over the
$\mathbf{Z}_{p}$
-anticyclotomic extension of
$K$
. |
---|---|
ISSN: | 1474-7480 1475-3030 |
DOI: | 10.1017/S147474801500016X |