Nontrivial elements of Sha explained through K3 surfaces
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Publication:3055103
DOI10.1090/S0025-5718-08-02105-4zbMath1215.11059arXiv0706.0541MaRDI QIDQ3055103
Publication date: 7 November 2010
Published in: Mathematics of Computation (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0706.0541
(K3) surfaces and Enriques surfaces (14J28) Abelian varieties of dimension (> 1) (11G10) Jacobians, Prym varieties (14H40) Elliptic surfaces, elliptic or Calabi-Yau fibrations (14J27) Varieties over global fields (11G35) Arithmetic ground fields for surfaces or higher-dimensional varieties (14J20) Arithmetic ground fields for abelian varieties (14K15) Global ground fields in algebraic geometry (14G25)
Related Items
Homogeneous spaces and degree 4 del Pezzo surfaces ⋮ Transcendental obstructions to weak approximation on general \(K3\) surfaces ⋮ Rational points on curves ⋮ Explicit computations on the desingularized Kummer surface ⋮ Tate-Shafarevich groups and $K3$ surfaces ⋮ Brauer-Manin obstructions on degree 2 \(K3\) surfaces ⋮ Failure of the Hasse principle on general surfaces
Cites Work
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- Exhibiting SHA[2 on hyperelliptic Jacobians]
- An elliptic \(K3\) surface associated to Heron triangles
- \(K3\) surfaces with Picard number one and infinitely many rational points
- Enriques' classification of surfaces in char p. III
- Computing a Selmer group of a Jacobian using functions on the curve
- On K3 surfaces with large Picard number
- The Cassels-Tate pairing on polarized Abelian varieties
- Brauer groups of diagonal quartic surfaces
- Implementing 2-descent for Jacobians of hyperelliptic curves
- The Brauer–Manin obstruction on del Pezzo surfaces of degree 2 branched along a plane section of a Kummer surface
- Computing the BrauerManin obstructions
