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arXiv · 1403.2924

Two torsion in the Brauer group of a hyperelliptic curve

Brendan Creutz·Bianca Viray
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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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Brendan Creutz, Bianca Viray. 2014-03-12. Two torsion in the Brauer group of a hyperelliptic curve. https://doi.org/10.1007/s00229-014-0721-7

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