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arXiv · 1707.08330

On some algebras associated to genus one curves

Tom Fisher
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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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Tom Fisher. 2017-07-26. On some algebras associated to genus one curves. https://arxiv.org/abs/1707.08330

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