$2$-Torsion of the Brauer Group of an Elliptic Curve: Generators and Relations

In this paper we describe the $2$-torsion part of the Brauer group ${\rm Br}\,E$ of an elliptic curve $E$ defined over an arbitrary field of characteristic $\not= 2$ in terms of generators and relations.

2000 Mathematics Subject Classification: 14H52, 16H05, 16K20

Keywords and Phrases: Elliptic curves, Brauer groups.

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