scientific article; zbMATH DE number 1368944
From MaRDI portal
Publication:4702588
zbMath0946.11027arXivmath/9809206MaRDI QIDQ4702588
Publication date: 25 October 2000
Full work available at URL: https://arxiv.org/abs/math/9809206
Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Manin's conjectureIwasawa theoryelliptic curveSelmer groupsBirch-Swinnerton-Dyer conjectureTate periodelliptic main conjectureSaint-Etienne theorem
Galois cohomology (11S25) Elliptic curves over global fields (11G05) Iwasawa theory (11R23) Zeta functions and (L)-functions (11S40)
Related Items
Euler characteristics and their congruences for multisigned Selmer groups ⋮ Variation of Iwasawa invariants in Hida families ⋮ Finite \(\Lambda\)-submodules of Selmer groups of Abelian varieties over cyclotomic \(\mathbb Z_p\)-extensions. ⋮ Asymptotic growth of Mordell–Weil ranks of elliptic curves in noncommutative towers ⋮ On the algebraic functional equation of the eigenspaces of mixed signed Selmer groups of elliptic curves with good reduction at primes above \(p\) ⋮ On the weak Leopoldt conjecture and coranks of Selmer groups of supersingular abelian varieties in \(p\)-adic Lie extensions ⋮ SELMER GROUPS OF ELLIPTIC CURVES OVER THE EXTENSION ⋮ On the Birch and Swinnerton-Dyer conjecture for modular elliptic curves over totally real fields ⋮ An Introduction to p-Adic Hodge Theory ⋮ Selmer groups for elliptic curves in \(\mathbb Z_l^d \)-extensions of function fields of characteristic \(p\) ⋮ Congruences between Ramanujan's tau function and elliptic curves, and Mazur-Tate elements at additive primes ⋮ Mordell–Weil ranks and Tate–Shafarevich groups of elliptic curves with mixed-reduction type over cyclotomic extensions ⋮ On the structure of Selmer groups over 𝑝-adic Lie extensions ⋮ On analogues of Mazur-Tate type conjectures in the Rankin-Selberg setting ⋮ Iwasawa invariants for elliptic curves over \(\mathbb{Z}_p\)-extensions and Kida's formula ⋮ On order of vanishing of characteristic elements ⋮ Eisenstein congruence on unitary groups and Iwasawa main conjectures for CM fields ⋮ Fitting ideals in two-variable equivariant Iwasawa theory and an application to CM elliptic curves ⋮ On the cohomology of Kobayashi’s plus/minus norm groups and applications ⋮ Euler characteristic and Akashi series for Selmer groups over global function fields ⋮ On the indivisibility of derived Kato's Euler systems and the main conjecture for modular forms ⋮ On the \(\mu\)-invariant of fine Selmer groups ⋮ Ranks of the rational points of abelian varieties over ramified fields, and Iwasawa theory for primes with non-ordinary reduction ⋮ Residual supersingular Iwasawa theory and signed Iwasawa invariants ⋮ On free resolutions of Iwasawa modules ⋮ Asymptotic formula for Tate-Shafarevich groups of \(p\)-supersingular elliptic curves over anticyclotomic extensions ⋮ Arithmetic statistics and Diophantine stability for elliptic curves ⋮ On the modularity of elliptic curves over the cyclotomic \(\mathbb{Z}_p\)-extension of some real quadratic fields ⋮ Nonvanishing of Hecke \(L\)-functions and the Bloch-Kato conjecture ⋮ Arithmetic properties of signed Selmer groups at non-ordinary primes ⋮ The vanishing of anticyclotomic \(\mu\)-invariants for non-ordinary modular forms ⋮ REMARKS ON HILBERT’S TENTH PROBLEM AND THE IWASAWA THEORY OF ELLIPTIC CURVES ⋮ RANK JUMPS AND GROWTH OF SHAFAREVICH–TATE GROUPS FOR ELLIPTIC CURVES IN -EXTENSIONS ⋮ Selmer Groups and AnticyclotomicZp-extensions ⋮ \(\lambda\)-invariant stability in families of modular Galois representations ⋮ On the Iwasawa invariants of BDP Selmer groups and BDP \(p\)-adic \(L\)-functions ⋮ Mazur-Tate elements of nonordinary modular forms ⋮ Structure of fine Selmer groups in abelian \(p\)-adic Lie extensions ⋮ On the \(p\)-adic \(L\)-function of a modular form at a supersingular prime ⋮ The Iwasawa Main Conjectures for \(\mathrm{GL}_{2}\) ⋮ Bianchi modular symbols and \(p\)-adic \(L\)-functions ⋮ On the anticyclotomic Iwasawa main conjecture for Hilbert modular forms of parallel weights ⋮ Iwasawa \(\mu\)-invariants of elliptic curves and their symmetric powers. ⋮ Congruences with Eisenstein series and -invariants ⋮ On the control theorem for fine Selmer groups and the growth of fine Tate-Shafarevich groups in \(\mathbb{Z}_p\)-extensions ⋮ Torsion groups of elliptic curves over the \(\mathbb{Z}_p\)-extensions of \(\mathbb{Q}\) ⋮ Congruences between Selmer groups ⋮ On a new invariant determining the isomorphism classes of \(\Lambda\)-modules with \(\lambda = 3\) ⋮ The Eisenstein ideal with squarefree level ⋮ On the Hida deformations of fine Selmer groups ⋮ Iwasawa Theory, projective modules, and modular representations ⋮ Root numbers, Selmer groups, and non-commutative Iwasawa theory ⋮ Construction of elliptic curves with large Iwasawa \(\lambda\)-invariants and large Tate-Shafarevich groups ⋮ Fine Selmer groups, Heegner points and anticyclotomic ℤp-extensions ⋮ Ranks of \(\mathrm{GL}_2\) Iwasawa modules of elliptic curves ⋮ On the plus and the minus Selmer groups for elliptic curves at supersingular primes ⋮ Heegner point Kolyvagin system and Iwasawa main conjecture ⋮ Root numbers and parity of local Iwasawa invariants ⋮ Elliptic curves over \(\mathbb{Q}_\infty\) are modular ⋮ An algebraic version of a theorem of Kurihara ⋮ Anomalous primes of the elliptic curveED: y2=x3+D ⋮ \(p^r\)-Selmer companion modular forms ⋮ Plus/minus Selmer groups and anticyclotomic \(\mathbb{Z}_p\)-extensions ⋮ On the algebraic functional equation for the mixed signed Selmer group over multiple $\mathbb {Z}_{p}$-extensions ⋮ Variation of the algebraic λ-invariant over a solvable extension ⋮ Ranks of rational points of the Jacobian varieties of hyperelliptic curves ⋮ Iwasawa theory for Artin representations. I ⋮ Equivariant Iwasawa theory for elliptic curves ⋮ Constructing plus/minus local points over Iwasawa Kummer extensions, and Iwasawa theory for supersingular reduction ⋮ Parity of ranks of elliptic curves with equivalent mod 𝑝 Galois representations ⋮ Some remarks on Kida's formula when \(\mu\neq 0\) ⋮ On the Mordell-Weil ranks of supersingular abelian varieties in cyclotomic extensions ⋮ Structure of the Mordell-Weil group over the ℤ_{𝕡}-extensions ⋮ The symmetric structure of the plus/minus Selmer groups of elliptic curves over totally real fields and the parity conjecture ⋮ On the structure of signed Selmer groups ⋮ ON THE EULER CHARACTERISTICS OF SIGNED SELMER GROUPS ⋮ Iwasawa invariants for the false-Tate extension and congruences between modular forms ⋮ ON THE SELMER GROUP OF A CERTAIN -ADIC LIE EXTENSION ⋮ Anticyclotomic \(\mu \)-invariants of residually reducible Galois representations ⋮ On the anticyclotomic Iwasawa theory of rational elliptic curves at Eisenstein primes ⋮ Conjecture a and \(\mu\)-invariant for Selmer groups of supersingular elliptic curves ⋮ Algorithms for the arithmetic of elliptic curves using Iwasawa theory ⋮ Selmer groups in Iwasawa theory and congruences ⋮ Arithmetic statistics and noncommutative Iwasawa theory ⋮ \(p^{\infty}\)-Selmer groups and rational points on CM elliptic curves ⋮ Towards Hilbert's tenth problem for rings of integers through Iwasawa theory and Heegner points ⋮ On the signed Selmer groups of congruent elliptic curves with semistable reduction at all primes above $p$ ⋮ Iwasawa invariants of Galois deformations ⋮ Euler characteristics and their congruences in the positive rank setting ⋮ Bounding the Iwasawa invariants of Selmer groups ⋮ Overview of Some Iwasawa Theory ⋮ The Structure of Selmer Groups of Elliptic Curves and Modular Symbols ⋮ Finite submodules and Iwasawa \(\mu\)-invariants ⋮ \(\Lambda\)-submodules of finite index of anticyclotomic plus and minus Selmer groups of elliptic curves ⋮ Congruences Between Modular Forms and the Birch and Swinnerton-Dyer Conjecture ⋮ On the Structure of Selmer Groups ⋮ Kolyvagin's work and anticyclotomic tower fields: the supersingular case ⋮ Rank parity for congruent supersingular elliptic curves