The Brauer group of Kummer surfaces and torsion of elliptic curves

DOI10.1515/CRELLE.2011.121zbMath1256.14036arXiv0911.2261OpenAlexW2963776088WikidataQ57395840 ScholiaQ57395840MaRDI QIDQ2890362

Alexei N. Skorobogatov, Yuri G. Zarhin

Publication date: 8 June 2012

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/0911.2261

zbMATH Keywords

rational pointsBrauer groupKummer surfacetorsion of elliptic curves

Mathematics Subject Classification ID

Rational points (14G05) (K3) surfaces and Enriques surfaces (14J28) Arithmetic ground fields for surfaces or higher-dimensional varieties (14J20) Global ground fields in algebraic geometry (14G25)

Related Items (13)

Iterating the algebraic étale-Brauer set ⋮ Explicit uniform bounds for Brauer groups of singular \(K3\) surfaces ⋮ Odd torsion Brauer elements and arithmetic of diagonal quartic surfaces over number fields ⋮ Weak approximation for 0-cycles on a product of elliptic curves ⋮ Transcendental obstructions to weak approximation on general \(K3\) surfaces ⋮ Odd order Brauer-Manin obstruction on diagonal quartic surfaces ⋮ ABELIAN -DIVISION FIELDS OF ELLIPTIC CURVES AND BRAUER GROUPS OF PRODUCT KUMMER & ABELIAN SURFACES ⋮ Arithmetic of K3 Surfaces ⋮ Good reduction of the Brauer–Manin obstruction ⋮ Complex multiplication and Brauer groups of \(K3\) surfaces ⋮ On Brauer groups of double covers of ruled surfaces ⋮ Pairs of elliptic curves with maximal Galois representations ⋮ On cubic torsors, biextensions and Severi-Brauer varieties over abelian varieties

Uses Software

• SageMath

Cites Work

• Rational isogenies of prime degree. (With an appendix by D. Goldfeld)
• Galois properties of points of finite order of elliptic curves
• 2-descent on elliptic curves and rational points on certain Kummer surfaces
• Mod $2$ representations of elliptic curves
• Unnamed Item

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