Iwasawa theory of elliptic curves at supersingular primes over ℤ p -extensions of number fields
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Publication:3413795
DOI10.1515/CRELLE.2006.069zbMath1114.11053arXivmath/0411496OpenAlexW2039569224MaRDI QIDQ3413795
Publication date: 18 December 2006
Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0411496
Elliptic curves over global fields (11G05) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Iwasawa theory (11R23) Elliptic curves over local fields (11G07)
Related Items (31)
Euler characteristics and their congruences for multisigned Selmer groups ⋮ On the parity of supersingular Weil polynomials ⋮ Mordell–Weil ranks and Tate–Shafarevich groups of elliptic curves with mixed-reduction type over cyclotomic extensions ⋮ On analogues of Mazur-Tate type conjectures in the Rankin-Selberg setting ⋮ Plus and minus logarithms and Amice transform ⋮ Residual supersingular Iwasawa theory and signed Iwasawa invariants ⋮ Asymptotic formula for Tate-Shafarevich groups of \(p\)-supersingular elliptic curves over anticyclotomic extensions ⋮ On the modularity of elliptic curves over the cyclotomic \(\mathbb{Z}_p\)-extension of some real quadratic fields ⋮ Supersingular elliptic curves over \(\mathbb{Z}_p\)-extensions ⋮ On the Iwasawa theory of CM fields for supersingular primes ⋮ Iwasawa theory for elliptic curves at supersingular primes: a pair of Main Conjectures ⋮ The \(p\)-adic Gross-Zagier formula for elliptic curves at supersingular primes ⋮ Anticyclotomic Iwasawa theory of abelian varieties of \(\mathrm{GL}_2\)-type at non-ordinary primes ⋮ Solvable points on genus one curves ⋮ Plus/minus \(p\)-adic \(L\)-functions for Hilbert modular forms ⋮ On Selmer groups in the supersingular reduction case ⋮ Fine Selmer groups, Heegner points and anticyclotomic ℤp-extensions ⋮ On the plus and the minus Selmer groups for elliptic curves at supersingular primes ⋮ An algebraic version of a theorem of Kurihara ⋮ Coleman maps for modular forms at supersingular primes over Lubin-Tate extensions ⋮ Plus/minus Selmer groups and anticyclotomic \(\mathbb{Z}_p\)-extensions ⋮ Equivariant Iwasawa theory for elliptic curves ⋮ On the structure of signed Selmer groups ⋮ On anticyclotomic μ-invariants of modular forms ⋮ Plus/minus Heegner points and Iwasawa theory of elliptic curves at supersingular primes ⋮ On the norm maps of formal groups for \(\mathbb Z_{p}\)-extensions ⋮ Iwasawa theory of the fine Selmer group ⋮ Bounding the Iwasawa invariants of Selmer groups ⋮ \(\Lambda\)-submodules of finite index of anticyclotomic plus and minus Selmer groups of elliptic curves ⋮ On the freeness of anticyclotomic Selmer groups of modular forms ⋮ Kolyvagin's work and anticyclotomic tower fields: the supersingular case
Cites Work
- 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
- \(p\)-adic height pairings. II
- On norm maps for one dimensional formal groups. III
- Iwasawa theory of \(p\)-adic representations over a local field
- Iwasawa theory for elliptic curves at supersingular primes
- On the Tate-Shafarevich groups over cyclotomic fields of an elliptic curve with supersingular reduction. I.
- On the \(p\)-adic \(L\)-function of a modular form at a supersingular prime
- Uniform distribution of Heegner points.
- Mazur's conjecture on higher Heegner points.
- An algebraic version of a theorem of Kurihara
- Special values of anticyclotomic \(L\)-functions.
- Rational points of Abelian varieties with values in towers of number fields
- On the Birch and Swinnerton-Dyer conjecture
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