On some algebras associated to genus one curves
JOURNAL OF ALGEBRA
MetadataShow full item record
Fisher, T. (2019). On some algebras associated to genus one curves. JOURNAL OF ALGEBRA, 518 519-541. https://doi.org/10.1016/j.jalgebra.2018.09.011
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-Châtelet and Brauer groups of an elliptic curve.
Elliptic curves, Brauer groups, Azurnaya algebras, Quadric intersections
External DOI: https://doi.org/10.1016/j.jalgebra.2018.09.011
This record's URL: https://www.repository.cam.ac.uk/handle/1810/287581