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ON THE $p$-ADIC VARIATION OF HEEGNER POINTS

Published online by Cambridge University Press:  18 February 2019

Francesc Castella*
Affiliation:
Mathematics Department, Princeton University, Fine Hall, Princeton, NJ 08544-1000, USA (fcabello@math.princeton.edu)

Abstract

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.

Type
Research Article
Copyright
© Cambridge University Press 2019

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Footnotes

The author was supported in part by NSF grant DMS-1801385. This project received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 682152).

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ON THE $p$-ADIC VARIATION OF HEEGNER POINTS
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