A \(p\)-adic Waldspurger formula and the conjecture of Birch and Swinnerton-Dyer
From MaRDI portal
Publication:6190071
DOI10.1007/s41745-022-00313-0OpenAlexW4295943205MaRDI QIDQ6190071
Publication date: 5 March 2024
Published in: Journal of the Indian Institute of Science (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s41745-022-00313-0
Elliptic curves over global fields (11G05) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) Arithmetic aspects of modular and Shimura varieties (11G18) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Iwasawa theory (11R23)
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
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Multiplicative reduction and the cyclotomic main conjecture for \(\mathrm{GL}_2\)
- Iwasawa theory and motivic \(L\)-functions
- Torsion points on curves and p-adic abelian integrals
- Heegner points and derivatives of \(L\)-series
- Tate-Shafarevich groups and L-functions of elliptic curves with complex multiplication
- Points de Heegner et dérivées de fonctions L p-adiques. (Heegner points and derivatives of p-adic L-functions)
- The ``main conjectures of Iwasawa theory for imaginary quadratic fields
- \(p\)-adic \(L\)-functions and rational points on elliptic curves with complex multiplication
- The arithmetic of elliptic curves
- On the conjecture of Birch and Swinnerton-Dyer
- Modular curves and the Eisenstein ideal
- Iwasawa theory and \(p\)-adic Hodge theory
- Iwasawa theory for elliptic curves at supersingular primes
- On the Iwasawa invariants of elliptic curves
- The Birch and Swinnerton-Dyer formula for elliptic curves of analytic rank one
- Modular elliptic curves and Fermat's Last Theorem
- 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
- Anticyclotomic main conjecture for modular forms and integral Perrin-Riou twists
- 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
- Iwasawa main conjecture for Rankin-Selberg \(p\)-adic \(L\)-functions
- The even parity Goldfeld conjecture: congruent number elliptic curves
- A proof of Perrin-Riou's Heegner point main conjecture
- Ternary cubic forms having bounded invariants, and the existence of a positive proportion of elliptic curves having rank 0
- Selmer groups and the indivisibility of Heegner points
- 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
- The Iwasawa Main Conjectures for \(\mathrm{GL}_{2}\)
- Congruent numbers and Heegner points
- Nonvanishing theorems for L-functions of modular forms and their derivatives
- Diophantine analysis and modular forms
- 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
- Anticyclotomic p-adic L-function of Central Critical Rankin-Selberg L-value
- A positive proportion of elliptic curves over $\mathbb{Q}$ have rank one
- Global divisibility of Heegner points and Tamagawa numbers
- Fonctions $L$ $p$-adiques, théorie d'Iwasawa et points de Heegner
- Zeroes of zeta functions and symmetry
- 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
- The Birch and Swinnerton-Dyer Conjecture: A brief survey
- Heights of Heegner points on Shimura curves.
This page was built for publication: A \(p\)-adic Waldspurger formula and the conjecture of Birch and Swinnerton-Dyer
