Galois properties of torsion points on abelian varieties
From MaRDI portal
Publication:1157371
DOI10.1007/BF01394256zbMath0471.14023MaRDI QIDQ1157371
Publication date: 1981
Published in: Inventiones Mathematicae (Search for Journal in Brave)
Full work available at URL: https://eudml.org/doc/142785
Elliptic curves (14H52) Arithmetic ground fields for abelian varieties (14K15) Global ground fields in algebraic geometry (14G25) Formal groups, (p)-divisible groups (14L05)
Related Items (71)
Geometric quadratic Chabauty over number fields ⋮ On Higher Congruences Between Cusp Forms and Eisenstein Series. II. ⋮ Quadratic points on bielliptic modular curves ⋮ A criterion to rule out torsion groups for elliptic curves over number fields ⋮ Local-global properties of torsion points on three-dimensional abelian varieties ⋮ Integration of Algebraic Functions ⋮ Comments on Integration of Algebraic Functions ⋮ Splitting of primes in number fields generated by points on some modular curves ⋮ Elliptic curves over totally real quartic fields not containing √5 are modular ⋮ On a probabilistic local-global principle for torsion on elliptic curves ⋮ On the local-global divisibility over abelian varieties ⋮ Visible evidence for the Birch and Swinnerton-Dyer conjecture for modular abelian varieties of analytic rank zero ⋮ A Table of Elliptic Curves over the Cubic Field of Discriminant–23 ⋮ On Ribet’s isogeny for $J_0(65)$ ⋮ Cycles of quadratic polynomials and rational points on a genus-2 curve ⋮ On the cyclic torsion of elliptic curves over cubic number fields ⋮ Unisingular representations in arithmetic and Lie theory ⋮ Torsion sections of Abelian fibrations ⋮ Purely additive reduction of abelian varieties with torsion ⋮ -adic images of Galois for elliptic curves over (and an appendix with John Voight) ⋮ SYMPLECTIC STABILIZERS WITH APPLICATIONS TO ABELIAN VARIETIES ⋮ Realizations of unisingular representations by hyperelliptic Jacobians ⋮ Examples of non-simple abelian surfaces over the rationals with non-square order Tate-Shafarevich group ⋮ On reduction maps and arithmetic dynamics of Mordell–Weil type groups ⋮ Eventually stable quadratic polynomials over \(\mathbb{Q}\) ⋮ Asymptotic Fermat for signature \((4, 2, p)\) over number fields ⋮ The rational torsion subgroup of \(J_0(N)\) ⋮ Torsion groups of elliptic curves over ℚ(μp∞) ⋮ On a local-global principle for quadratic twists of abelian varieties ⋮ Gonality of the modular curve 𝑋₀(𝑁) ⋮ On the local-global principle for isogenies of abelian surfaces ⋮ On the cyclic torsion of elliptic curves over cubic number fields. II ⋮ On Ribet's lemma for \(\mathrm{GL}_2\) modulo prime powers ⋮ Elliptic curves over totally real cubic fields are modular ⋮ Determination of the modular Jacobian varieties \(J_1(M,MN)\) with the Mordell-Weil rank zero ⋮ A descent map for curves with totally degenerate semi-stable reduction ⋮ Composite images of Galois for elliptic curves over $\mathbf {Q}$ and entanglement fields ⋮ Quadratic points on modular curves ⋮ Component group of the \(p\)-new subvariety of \(J_0 (Mp)\) ⋮ Examples of abelian surfaces failing the local-global principle for isogenies ⋮ Sporadic cubic torsion ⋮ Classifying Galois groups of small iterates via rational points ⋮ A REFINEMENT OF KOBLITZ'S CONJECTURE ⋮ Galois criterion for torsion points of Drinfeld modules ⋮ Explicit application of Waldspurger’s theorem ⋮ Computing Torsion Points on Curves ⋮ On some congruence properties of elliptic curves ⋮ Minimal Torsion in Isogeny Classes of Elliptic Curves ⋮ A local-global principle for rational isogenies of prime degree ⋮ Torsion on elliptic curves in isogeny classes ⋮ Points of small order on three-dimensional abelian varieties; with an appendix by Yuri Zarhin ⋮ A computational approach to the 2-torsion structure of abelian threefolds ⋮ Splitting of abelian varieties ⋮ Unnamed Item ⋮ Selmer groups of twists of elliptic curves over \(K\) with \(K\)-rational torsion points ⋮ On ternary Diophantine equations of signature(p,p,2)over number fields ⋮ Rational torsion of generalized Jacobians of modular and Drinfeld modular curves ⋮ On a Hasse principle for Mordell-Weil groups ⋮ A local-global principle for isogenies of prime degree over number fields ⋮ Fixed-point subgroups of \(\text{GL}_3({q})\) ⋮ Quasimodular moonshine and arithmetic connections ⋮ Equidistribution Questions for Universal Extensions ⋮ Semistable reduction of abelian varieties over extensions of small degree ⋮ The arithmetic of curves defined by iteration ⋮ Eisenstein ideals and the rational torsion subgroups of modular Jacobian varieties. II. ⋮ Linear relations and arithmetic on abelian schemes ⋮ Local-global questions for divisibility in commutative algebraic groups ⋮ Unipotent groups associated to reduced curves ⋮ Rational points on conic bundles over elliptic curves ⋮ Divisibility of torsion subgroups of abelian surfaces over number fields ⋮ Tamagawa Numbers of elliptic curves with 𝐶₁₃ torsion over quadratic fields
Cites Work
This page was built for publication: Galois properties of torsion points on abelian varieties
