The Hasse problem for rational surfaces.

DOI10.1515/crll.1975.274-275.164zbMath0326.14007OpenAlexW98659626WikidataQ104089867 ScholiaQ104089867MaRDI QIDQ4090458

B. J. Birch, H. P. F. Swinnerton-Dyer

Publication date: 1974

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://www.digizeitschriften.de/dms/resolveppn/?PPN=GDZPPN002190516

Mathematics Subject Classification ID

Rational and unirational varieties (14M20) Cubic and quartic Diophantine equations (11D25) Global ground fields in algebraic geometry (14G25) Special surfaces (14J25)

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Zeros of pairs of quadratic forms ⋮ Exhibiting SHA[2 on hyperelliptic Jacobians] ⋮ Del Pezzo surfaces of degree four violating the Hasse principle are Zariski dense in the moduli scheme ⋮ Homogeneous spaces and degree 4 del Pezzo surfaces ⋮ La descente sur les variétés rationnelles. II. (The descent on rational varieties. II) ⋮ Quadratic points on intersections of two quadrics ⋮ There are genus one curves violating Hasse principle over every number field ⋮ Rational points on the intersection of three quadrics ⋮ Failure of the Hasse principle for Enriques surfaces ⋮ Arithmetic of del Pezzo surfaces of degree 4 and vertical Brauer groups ⋮ Weak approximation for surfaces defined by two quadratic forms ⋮ Weak approximation on del Pezzo surfaces of degree 1 ⋮ The arithmetic of certain del Pezzo surfaces and \(K3\) surfaces ⋮ Rationality of complete intersections of two quadrics over nonclosed fields ⋮ On the Frequency of Algebraic Brauer Classes on Certain Log K3 Surfaces

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