Rational points on some pencils of conics with 6 singular fibres

DOI10.5802/afst.935zbMath0976.14014OpenAlexW2318540742MaRDI QIDQ1576414

H. P. F. Swinnerton-Dyer

Publication date: 13 November 2000

Published in: Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AFST_1999_6_8_2_331_0

zbMATH Keywords

weak approximationHasse principleBrauer-Manin obstructionpencil of conicsuniversal torsor

Mathematics Subject Classification ID

Rational points (14G05) Varieties over global fields (11G35) Diophantine equations in many variables (11D72) Pencils, nets, webs in algebraic geometry (14C21)

Related Items (6)

The Brauer group of torsors and its arithmetic applications. ⋮ Schinzel hypothesis on average and rational points ⋮ Hashing to elliptic curves through Cipolla-Lehmer-Müller's square root algorithm ⋮ Brauer–Manin obstruction and families of generalised Châtelet surfaces over number fields ⋮ Rational points on pencils of conics and quadrics with many degenerate fibres ⋮ Rational points on fibrations with few non-split fibres

Cites Work

• La descente sur les variétés rationnelles. II. (The descent on rational varieties. II)
• The Brauer group of cubic surfaces
• Hasse principle and weak approximation for pencils of Severi-Brauer and similar varieties.
• Unnamed Item
• Unnamed Item

This page was built for publication: Rational points on some pencils of conics with 6 singular fibres