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• W2074969868 abstract "Let k be a field of characteristic not two. To each irreducible quartic f ( x ) over k we associate a certain algebra A f , given by explicit generators and relations. We prove A f is an Azumaya algebra of rank four over its center and that its center is the coordinate ring of an affine piece of an elliptic curve, the Jacobian of the curve C : y 2 = f ( x ) . Its simple images are quaternion algebras and the resulting function from the group of k -rational points on the Jacobian to the Brauer group of k is a group homomorphism whose image is the relative Brauer group of central simple k -algebra split by the function field of C . We also show that the algebra A f is split if and only if C has a k -rational point." @default.
• W2074969868 created "2016-06-24" @default.
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• W2074969868 date "2007-07-01" @default.
• W2074969868 modified "2023-09-27" @default.
• W2074969868 title "On an algebra determined by a quartic curve of genus one" @default.
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• W2074969868 doi "https://doi.org/10.1016/j.jalgebra.2006.10.024" @default.
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