Tate-Shafarevich groups and $K3$ surfaces

DOI10.1090/S0025-5718-09-02264-9zbMath1200.14056arXiv0711.4436MaRDI QIDQ3584791

Patrick Corn

Publication date: 30 August 2010

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0711.4436

zbMATH Keywords

\(K3\) surfacesTate-Shafarevich groupBrauer-Manin obstructiongenus 2 curves

Mathematics Subject Classification ID

(K3) surfaces and Enriques surfaces (14J28) Abelian varieties of dimension (> 1) (11G10) Jacobians, Prym varieties (14H40) [https://zbmath.org/classification/?q=cc:11G30 Curves of arbitrary genus or genus ( e 1) over global fields (11G30)] Varieties over global fields (11G35) Global ground fields in algebraic geometry (14G25)

Related Items

Implementation and efficiency analysis of an adaptive \textit{hp}-finite element method for solving boundary value problems for the stationary reaction-diffusion equation ⋮ Homogeneous spaces and degree 4 del Pezzo surfaces ⋮ Transcendental obstructions to weak approximation on general \(K3\) surfaces ⋮ Explicit computations on the desingularized Kummer surface ⋮ Brauer-Manin obstructions on degree 2 \(K3\) surfaces ⋮ Failure of the Hasse principle on general surfaces

Uses Software

• Magma

Cites Work

• Exhibiting SHA[2 on hyperelliptic Jacobians]
• The Magma algebra system. I: The user language
• Del Pezzo surfaces of degree 6
• The Cassels-Tate pairing on polarized Abelian varieties
• Implementing 2-descent for Jacobians of hyperelliptic curves
• Nontrivial elements of Sha explained through K3 surfaces
• The Brauer-Manin Obstruction and III[2]
• Efficient evaluation of the Brauer–Manin obstruction
• On the arithmetic of del Pezzo surfaces of degree 2
• The Brauer-Manin obstruction on Del Pezzo surfaces of degree 2
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