On the non-vanishing of p -adic heights on CM abelian varieties, and the arithmetic of Katz p -adic L -functions
- Award ID(s):
- 2001409
- NSF-PAR ID:
- 10250036
- Date Published:
- Journal Name:
- Annales de l'Institut Fourier
- Volume:
- 70
- Issue:
- 5
- ISSN:
- 1777-5310
- Page Range / eLocation ID:
- 2077 to 2101
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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In this paper, we prove an ‘explicit reciprocity law’ relating Howard’s system of big Heegner points to a two-variable p-adic L-function (constructed here) interpolating the p-adic Rankin L-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.more » « less