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On some algebras associated to genus one curves

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.


On some algebras associated to genus one curves   (20 pages)     dvi   ps   ps.gz   pdf

A Magma file checking the calculations in this paper is available here.