\(p\)-converse to a theorem of Gross-Zagier, Kolyvagin and Rubin
From MaRDI portal
Publication:2304172
DOI10.1007/s00222-019-00929-7zbMath1452.11068OpenAlexW2983595752WikidataQ126845898 ScholiaQ126845898MaRDI QIDQ2304172
Publication date: 6 March 2020
Published in: Inventiones Mathematicae (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00222-019-00929-7
Elliptic curves over global fields (11G05) Complex multiplication and moduli of abelian varieties (11G15) Arithmetic aspects of modular and Shimura varieties (11G18) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40)
Related Items (12)
The Birch and Swinnerton-Dyer Conjecture: A brief survey ⋮ On the soft \(p\)-converse to a theorem of Gross-Zagier and Kolyvagin ⋮ The congruent number problem and elliptic curves ⋮ A \(p\)-adic Waldspurger formula and the conjecture of Birch and Swinnerton-Dyer ⋮ Anticyclotomic Iwasawa theory of abelian varieties of \(\mathrm{GL}_2\)-type at non-ordinary primes ⋮ The even parity Goldfeld conjecture: congruent number elliptic curves ⋮ Heegner point Kolyvagin system and Iwasawa main conjecture ⋮ On the non-vanishing of \(p\)-adic heights on CM abelian varieties, and the arithmetic of Katz \(p\)-adic \(L\)-functions ⋮ Rubin's conjecture on local units in the anticyclotomic tower at inert primes ⋮ On the anticyclotomic Iwasawa theory of rational elliptic curves at Eisenstein primes ⋮ \(p^{\infty}\)-Selmer groups and rational points on CM elliptic curves ⋮ The universal \(p\)-adic Gross-Zagier formula
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Explicit Gross-Zagier and Waldspurger formulae
- \(p\)-adic \(L\)-functions for CM fields
- Anticyclotomic Iwasawa theory of CM elliptic curves
- The Iwasawa \(\mu \)-invariant of \(p\)-adic Hecke \(L\)-functions
- On \(L\)-functions of elliptic curves and anticyclotomic towers
- Heegner points and derivatives of \(L\)-series
- Tate-Shafarevich groups and L-functions of elliptic curves with complex multiplication
- The ``main conjectures of Iwasawa theory for imaginary quadratic fields
- \(p\)-adic \(L\)-functions and rational points on elliptic curves with complex multiplication
- On the conjecture of Birch and Swinnerton-Dyer
- Mazur's conjecture on higher Heegner points.
- Special values of anticyclotomic \(L\)-functions.
- \(p\)-adic Rankin \(L\)-series and rational points on CM elliptic curves
- The \(p\)-adic Gross-Zagier formula for elliptic curves at supersingular primes
- Generalized Heegner cycles and \(p\)-adic Rankin \(L\)-series. With an appendix by Brian Conrad
- Heegner point Kolyvagin system and Iwasawa main conjecture
- On the non-vanishing of \(p\)-adic heights on CM abelian varieties, and the arithmetic of Katz \(p\)-adic \(L\)-functions
- Iwasawa main conjecture for Rankin-Selberg \(p\)-adic \(L\)-functions
- 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
- Twisting commutative algebraic groups
- The Iwasawa Main Conjectures for \(\mathrm{GL}_{2}\)
- On the \(\mu\)-invariant of anticyclotomic \(p\)-adic \(L\)-functions for CM fields
- Congruent numbers and Heegner points
- Nonvanishing theorems for L-functions of modular forms and their derivatives
- On the parity of ranks of Selmer groups II
- Non-triviality of generalised Heegner cycles over anticyclotomic towers: a survey
- On the -invariant of the cyclotomic derivative of a Katzp-adic -function
- ON THE NON-TRIVIALITY OF THE -ADIC ABEL–JACOBI IMAGE OF GENERALISED HEEGNER CYCLES MODULO , II: SHIMURA CURVES
- Local ε-Factors and Characters of GL(2)
- Fonctions $L$ $p$-adiques, théorie d'Iwasawa et points de Heegner
- The Heegner point Kolyvagin system
- The Gross-Zagier Formula on Shimura Curves
- On the non-triviality of the $p$-adic Abel–Jacobi image of generalised Heegner cycles modulo $p$, I: Modular curves
- Anti-cyclotomic Katz $p$-adic $L$-functions and congruence modules
- p-adic heights of Heegner points and Beilinson-Flach classes
- The -adic Gross–Zagier formula on Shimura curves
- Anticyclotomic main conjectures for CM modular forms
- Non-triviality of CM points in ring class field towers. With an appendix by Christophe Cornut.
This page was built for publication: \(p\)-converse to a theorem of Gross-Zagier, Kolyvagin and Rubin
