Let A be an elliptic curve over the rationals with multiplicative reduction at a prime p, and let K be a quadratic field in which p is inert. Under a generalized Heegner assumption, our previous contribution [5] to this volume attaches to (A, p, K) balanced diagonal classes in the Selmer groups of the p-adic Tate module of A over certain ring class fields of K. These classes are obtained as p-adic limits of geometric classes in the cohomology of higher-dimensional Kuga-Sato varieties. The main result of this paper relates these diagonal classes to p-adic logarithms of Heegner or Stark-Heegner points, depending on whether K is complex or real respectively.
BALANCED DIAGONAL CLASSES AND RATIONAL POINTS ON ELLIPTIC CURVES / M. Bertolini, M. Seveso, R. Venerucci. - In: ASTÉRISQUE. - ISSN 0303-1179. - 2022:434(2022), pp. 175-201. [10.24033/ast.1177]
BALANCED DIAGONAL CLASSES AND RATIONAL POINTS ON ELLIPTIC CURVES
M. BertoliniPrimo
;M. SevesoPenultimo
;R. VenerucciUltimo
2022
Abstract
Let A be an elliptic curve over the rationals with multiplicative reduction at a prime p, and let K be a quadratic field in which p is inert. Under a generalized Heegner assumption, our previous contribution [5] to this volume attaches to (A, p, K) balanced diagonal classes in the Selmer groups of the p-adic Tate module of A over certain ring class fields of K. These classes are obtained as p-adic limits of geometric classes in the cohomology of higher-dimensional Kuga-Sato varieties. The main result of this paper relates these diagonal classes to p-adic logarithms of Heegner or Stark-Heegner points, depending on whether K is complex or real respectively.File | Dimensione | Formato | |
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