Division Algebras on ${\Bbb P}^2$ of Odd Index, Ramified Along a Smooth Elliptic Curve Are Cyclic
Division Algebras on ${\Bbb P}^2$ of Odd Index, Ramified Along a Smooth Elliptic Curve Are Cyclic
Séminaires et Congrès | 1997
Anglais
The simplest non-trivial division algebras that can be constructed over a rational function field in two variables are those that ramify along a divisor of degree three. In this note we give a precise structure theorem for such division algebras. It follows in particular that they are cyclic if the ramification locus is singular or if the index is odd.
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