On some algebras associated to genus one curves

2017/07/26 by Fisher, Tom
#11G05 #14F22 #16H05 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1707.08330

Abstract

Haile, Han and Kuo have studied certain non-commutative algebras associated to a binary quartic or ternary cubic form. We extend their construction to pairs of quadratic forms in four variables, and conjecture a further generalisation to genus one curves of arbitrary degree. These constructions give an explicit realisation of an isomorphism relating the Weil-Chatelet and Brauer groups of an elliptic curve.

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