On some algebras associated to genus one curves
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Authors
Fisher, Tom
Publication Date
2019-01-15Journal Title
JOURNAL OF ALGEBRA
ISSN
0021-8693
Publisher
Elsevier BV
Volume
518
Pages
519-541
Type
Article
This Version
AM
Metadata
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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
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.
Keywords
Elliptic curves, Brauer groups, Azurnaya algebras, Quadric intersections
Identifiers
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
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