Hasse principle for pencils of curves of genus one whose Jacobians have rational 2-division points

DOI10.1007/s002220050274zbMath0924.14011OpenAlexW4235049643WikidataQ57395858 ScholiaQ57395858MaRDI QIDQ1283461

Jean-Louis Colliot-Thélène, H. P. F. Swinnerton-Dyer, Alexei N. Skorobogatov

Publication date: 5 August 1999

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s002220050274

zbMATH Keywords

cohomological Brauer groupBrauer-Manin obstruction to the Hasse principlefiniteness of Tate-Shafarevich group of an elliptic curvevertical Brauer-Manin obstructionZariski dense rational points

Mathematics Subject Classification ID

Rational points (14G05) Elliptic curves over global fields (11G05) Elliptic curves (14H52) [https://zbmath.org/classification/?q=cc:11G30 Curves of arbitrary genus or genus ( e 1) over global fields (11G30)] Brauer groups of schemes (14F22)

Related Items

Diagonal quartic surfaces and transcendental elements of the Brauer group, Descent on elliptic surfaces and arithmetic bounds for the Mordell-Weil rank, The solubility of diagonal cubic surfaces, Average Bateman–Horn for Kummer polynomials, Une liste de problèmes, The Brauer–Manin obstruction on del Pezzo surfaces of degree 2 branched along a plane section of a Kummer surface, A finiteness theorem for the Brauer group of abelian varieties and 𝐾3 surfaces, Arithmetic of del Pezzo surfaces of degree 4 and vertical Brauer groups, The effect of twisting on the 2-Selmer group, Integral points on conic log K3 surfaces, Brauer groups of diagonal quartic surfaces, Arithmetic of K3 Surfaces, 2-descent on elliptic curves and rational points on certain Kummer surfaces, Local-global questions for divisibility in commutative algebraic groups, On the finiteness of the Brauer group of an arithmetic scheme, The Cassels-Tate pairing and the Platonic solids., Hasse principle for intersections of two quadrics.