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.
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Bianca Viray was partially supported by NSF Grant DMS-1002933.
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Creutz, B., Viray, B. Two torsion in the Brauer group of a hyperelliptic curve. manuscripta math. 147, 139–167 (2015). https://doi.org/10.1007/s00229-014-0721-7
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DOI: https://doi.org/10.1007/s00229-014-0721-7