On anticyclotomic variants of the \(p\)-adic Birch and Swinnerton-Dyer conjecture

DOI10.5802/jtnb.1174zbMath1489.11081arXiv1910.08680OpenAlexW2980477275WikidataQ113689207 ScholiaQ113689207MaRDI QIDQ2073988

Francesc Castella, Adebisi Agboola

Publication date: 3 February 2022

Published in: Journal de Théorie des Nombres de Bordeaux (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1910.08680

zbMATH Keywords

elliptic curvesHeegner points\(p\)-adic \(L\)-functionsBirch and Swinnerton-Dyer conjecture

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Iwasawa theory (11R23) Elliptic and modular units (11G16)

Related Items (2)

Asymptotic formula for Tate-Shafarevich groups of \(p\)-supersingular elliptic curves over anticyclotomic extensions ⋮ The universal \(p\)-adic Gross-Zagier formula

Cites Work

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• Heegner cycles and \(p\)-adic \(L\)-functions
• Iwasawa's main conjecture for elliptic curves over anticyclotonic \(\mathbb Z_p\)-extensions
• A refined conjecture of Mazur-Tate type for Heegner points
• Derived heights and generalized Mazur-Tate regulators
• Studying the growth of Mordell-Weil
• Mazur's conjecture on higher Heegner points.
• The Birch and Swinnerton-Dyer formula for elliptic curves of analytic rank one
• Iwasawa theory of Heegner points on abelian varieties of \(\text{GL}_2\) type
• \(p\)-adic Rankin \(L\)-series and rational points on CM elliptic curves
• Generalized Heegner cycles and \(p\)-adic Rankin \(L\)-series. With an appendix by Brian Conrad
• A proof of Perrin-Riou's Heegner point main conjecture
• Selmer groups and the indivisibility of Heegner points
• A converse to a theorem of Gross, Zagier, and Kolyvagin
• Rational points of Abelian varieties with values in towers of number fields
• On the parity of ranks of Selmer groups II
• On the modularity of elliptic curves over 𝐐: Wild 3-adic exercises
• Anticyclotomic p-adic L-function of Central Critical Rankin-Selberg L-value
• Bipartite Euler systems
• Derived P-Adic Heights
• ON THE -ADIC VARIATION OF HEEGNER POINTS
• p-adic heights of Heegner points and Beilinson-Flach classes
• On Rubin’s variant of the p-adic Birch and Swinnerton-Dyer conjecture
• Heegner points on Mumford-Tate curves

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