Arithmétique des courbes elliptiques à réduction supersingulière enp

DOI10.1080/10586458.2003.10504490zbMath1061.11031arXivmath/0109227OpenAlexW2091261565MaRDI QIDQ4811519

Bernadette Perrin-Riou

Publication date: 6 September 2004

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0109227

zbMATH Keywords

elliptic curvesIwasawa theoryTate-Shafarevich groupssupersingular reductioncyclotomic \(\mathbb Z_p\)-extensions

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)

Related Items (15)

On pairs of \(p\)-adic \(L\)-functions for weight-two modular forms ⋮ Congruences between Ramanujan's tau function and elliptic curves, and Mazur-Tate elements at additive primes ⋮ Iwasawa theory and p-adic L-functions over ${\mathbb Z}_{p}^{2}$-extensions ⋮ Arithmetic properties of signed Selmer groups at non-ordinary primes ⋮ The \(p\)-adic Gross-Zagier formula for elliptic curves at supersingular primes ⋮ Mazur-Tate elements of nonordinary modular forms ⋮ A formulation of \(p\)-adic versions of the Birch and Swinnerton-Dyer conjectures in the supersingular case ⋮ Root numbers and parity of local Iwasawa invariants ⋮ The Tate-Shafarevich group for elliptic curves with complex multiplication ⋮ On the Mordell-Weil ranks of supersingular abelian varieties in cyclotomic extensions ⋮ Rubin's conjecture on local units in the anticyclotomic tower at inert primes ⋮ Conjecture a and \(\mu\)-invariant for Selmer groups of supersingular elliptic curves ⋮ Algorithms for the arithmetic of elliptic curves using Iwasawa theory ⋮ On fine Selmer groups and the greatest common divisor of signed and chromatic 𝑝-adic 𝐿-functions ⋮ Rank parity for congruent supersingular elliptic curves

Uses Software

• PARI/GP
• ecdata

Cites Work

• Unnamed Item
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• Théorie d'Iwasawa p-adique locale et globale. (Local and global p-adic Iwasawa theory)
• On \(p\)-adic analogues of the conjectures of Birch and Swinnerton-Dyer
• Iwasawa theory and \(p\)-adic heights
• One-parametric \(p\)-adic subgroups of a group variety
• Unités cyclotomiques, unités semilocales et \(\mathbb{Z}_\ell\)-extensions. II
• \(p\)-adic \(L\)-functions of an elliptic curve and rational points
• Iwasawa theory of \(p\)-adic representations over a local field
• On the Tate-Shafarevich groups over cyclotomic fields of an elliptic curve with supersingular reduction. I.
• The \(p\)-adic sigma function
• Galois properties of points of finite order of elliptic curves
• Rational points of Abelian varieties with values in towers of number fields

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