Two torsion in the Brauer group of a hyperelliptic curve

Abstract

We construct unramified central simple algebras representing 2-torsion classes in the Brauer group of a hyperelliptic curve, and show that every 2-torsion class can be constructed this way when the curve has a rational Weierstrass point or when the base field is C_1. In general, we show that a large (but in general proper) subgroup of the 2-torsion classes are given by the construction. Examples demonstrating applications to the arithmetic of hyperelliptic curves defined over number fields are given.

25 pages. This was part I of arXiv:1306.3251v1; part II will be posted as arXiv:1306.3251v2

References in corpus (4)

• Two-cover descent on hyperelliptic curves
• Transcendental Brauer-Manin obstruction on a pencil of elliptic curves
• Locally trivial torsors that are not Weil-Châtelet divisible
• On Brauer groups of double covers of ruled surfaces

Cited by in corpus (1)

• On Brauer groups of double covers of ruled surfaces