On Brauer groups of double covers of ruled surfaces

Abstract

Let X be a smooth double cover of a geometrically ruled surface defined over a separably closed field of characteristic different from 2. The main result of this paper is a finite presentation of the 2-torsion in the Brauer group of X with generators given by central simple algebras over the function field of X and relations coming from the Néron-Severi group of X. In particular, the result gives a central simple algebra representative for the unique nontrivial Brauer class on any Enriques surface. An example demonstrating the applications to the study of rational points is given.

v3: Sections 4-6 expanded/rewritten

References in corpus (6)

• Two-cover descent on hyperelliptic curves
• Transcendental obstructions to weak approximation on general K3 surfaces
• Transcendental Brauer-Manin obstruction on a pencil of elliptic curves
• Failure of the Hasse principle on general K3 surfaces
• Two torsion in the Brauer group of a hyperelliptic curve
• Explicit descent in the Picard group of a cyclic cover of the projective line

Cited by in corpus (3)

• Two torsion in the Brauer group of a hyperelliptic curve
• Insufficiency of the Brauer-Manin obstruction for Enriques surfaces
• A transcendental Brauer-Manin obstruction to weak approximation on a Calabi-Yau threefold