On the vanishing of Selmer groups for elliptic curves over ring class fields
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Publication:1038485
DOI10.1016/j.jnt.2009.07.004zbMath1262.11068arXiv0806.4267OpenAlexW2964320618MaRDI QIDQ1038485
Publication date: 18 November 2009
Published in: Journal of Number Theory (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0806.4267
Elliptic curves over global fields (11G05) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40)
Related Items
Special values of anticyclotomic \(L\)-functions for modular forms, A refined Beilinson–Bloch conjecture for motives of modular forms, Selmer groups and central values of \(L\)-functions for modular forms, Quaternion algebras, Heegner points and the arithmetic of Hida families, A \(p\)-adic Maass-Shimura operator on Mumford curves, On the Bloch-Kato conjecture for Hilbert modular forms
Cites Work
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- Gross-Zagier formula for \(\text{GL}_ 2\).
- Iwasawa's main conjecture for elliptic curves over anticyclotonic \(\mathbb Z_p\)-extensions
- Heegner points and derivatives of \(L\)-series
- A rigid analytic Gross-Zagier formula and arithmetic applications. (With an appendix by B. Edixhoven)
- Schottky groups and Mumford curves
- Mean values of derivatives of modular \(L\)-series
- Test vectors for linear forms
- Heegner points, \(p\)-adic \(L\)-functions, and the Cherednik-Drinfeld uniformization
- On modular representations of \(\text{Gal}(\overline{\mathbb Q}/\mathbb Q)\) arising from modular forms
- Iwasawa-theory of abelian varieties at primes of non-ordinary reduction
- Galois properties of points of finite order of elliptic curves
- Rational points of Abelian varieties with values in towers of number fields
- Nonvanishing theorems for L-functions of modular forms and their derivatives
- The modular degree, congruence primes, and multiplicity one
- On the local divisibility of Heegner points
- Kolyvagin's descent and Mordell-Weil groups over ring class fields.
- Schémas en groupes de type $(p,\ldots,p)$
- THE ANTICYCLOTOMIC MAIN CONJECTURE FOR ELLIPTIC CURVES AT SUPERSINGULAR PRIMES
- Periodic flat modules, and flat modules for finite groups.
- Integration on \({\mathcal H_p}\times\mathcal H\) and arithmetic applications.