On the non-vanishing of \(p\)-adic heights on CM abelian varieties, and the arithmetic of Katz \(p\)-adic \(L\)-functions
From MaRDI portal
Publication:2027760
DOI10.5802/aif.3381zbMath1470.11185arXiv1803.09268OpenAlexW3156399440MaRDI QIDQ2027760
Ashay A. Burungale, Daniel Disegni
Publication date: 28 May 2021
Published in: Annales de l'Institut Fourier (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1803.09268
Abelian varieties of dimension (> 1) (11G10) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Heights (11G50)
Related Items (7)
The Iwasawa main conjectures for \(\operatorname{GL}_2\) and derivatives of \(p\)-adic \(L\)-functions ⋮ The Birch and Swinnerton-Dyer Conjecture: A brief survey ⋮ A \(p\)-adic Waldspurger formula and the conjecture of Birch and Swinnerton-Dyer ⋮ \(p\)-converse to a theorem of Gross-Zagier, Kolyvagin and Rubin ⋮ \(p^{\infty}\)-Selmer groups and rational points on CM elliptic curves ⋮ The universal \(p\)-adic Gross-Zagier formula ⋮ A note on rank one quadratic twists of elliptic curves and the non-degeneracy of 𝑝-adic regulators at Eisenstein primes
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- \(p\)-adic heights of Heegner points on Shimura curves
- \(p\)-adic \(L\)-functions for CM fields
- Anticyclotomic Iwasawa theory of CM elliptic curves
- The Iwasawa \(\mu \)-invariant of \(p\)-adic Hecke \(L\)-functions
- On \(p\)-adic absolute CM-periods. II
- \(p\)-adic height pairings. II
- Points de Heegner et dérivées de fonctions L p-adiques. (Heegner points and derivatives of p-adic L-functions)
- Automorphic forms and the periods of abelian varieties
- On some arithmetic properties of modular forms of one and several variables
- \(\mathfrak p\)-rigidity and Iwasawa \(\mu\)-invariants
- Every ordinary symplectic isogeny class in positive characteristic is dense in the moduli
- \(p\)-adic Rankin \(L\)-series and rational points on CM elliptic curves
- The \(p\)-adic Gross-Zagier formula for elliptic curves at supersingular primes
- Selmer groups and the indivisibility of Heegner points
- Horizontal non-vanishing of Heegner points and toric periods
- A converse to a theorem of Gross, Zagier, and Kolyvagin
- \(p\)-converse to a theorem of Gross-Zagier, Kolyvagin and Rubin
- A \(p\)-adic Waldspurger formula
- On the \(\mu\)-invariant of anticyclotomic \(p\)-adic \(L\)-functions for CM fields
- Non-triviality of generalised Heegner cycles over anticyclotomic towers: a survey
- On the -invariant of the cyclotomic derivative of a Katzp-adic -function
- Diagonal cycles and Euler systems II: The Birch and Swinnerton-Dyer conjecture for Hasse-Weil-Artin $L$-functions
- ON THE NON-TRIVIALITY OF THE -ADIC ABEL–JACOBI IMAGE OF GENERALISED HEEGNER CYCLES MODULO , II: SHIMURA CURVES
- ON TWISTED FORMS AND RELATIVE ALGEBRAIC K-THEORY
- Fonctions $L$ $p$-adiques, théorie d'Iwasawa et points de Heegner
- On Abelian Varieties with Complex Multiplication as Factors of the Jacobians of Shimura Curves
- 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
- The -adic Gross–Zagier formula on Shimura curves
- Non-triviality of CM points in ring class field towers. With an appendix by Christophe Cornut.
This page was built for publication: On the non-vanishing of \(p\)-adic heights on CM abelian varieties, and the arithmetic of Katz \(p\)-adic \(L\)-functions
