 Séminaires et Congrès - 2 - pages 43-53 | |
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Algèbre non commutative, groupes quantiques et invariants Septième contact Franco-Belge, Reims, Juin 1995
J. Alev, G. Cauchon (Éd.)
Séminaires et Congrès 2 (1997), 304 pages
Division Algebras on 
of Odd Index, Ramified Along a Smooth Elliptic Curve Are Cyclic
Michel Van den BERGH
Séminaires et Congrès 2 (1997), 43-53
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Résumé :
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.
Class. math. : 16K20, 13A20