On some algebras associated to genus one curves
Accepted version
Peer-reviewed
Repository URI
Repository DOI
Change log
Authors
Fisher, Torn
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-Châtelet and Brauer groups of an elliptic curve.
Description
Keywords
Elliptic curves, Brauer groups, Azurnaya algebras, Quadric intersections
Journal Title
JOURNAL OF ALGEBRA
Conference Name
Journal ISSN
0021-8693
1090-266X
1090-266X
Volume Title
518
Publisher
Elsevier BV