Division Algebras that Ramify Only Along a Singular Plane Cubic Curve

摘要

Let K be the field of rational functions in 2variables over an algebraically closed field k of characteristic 0. Let Dbe a finite dimensional K-central division algebra whose ramificationdivisor on the projective plane over k is a singular cubic curve. It isshown that D is cyclic and that the exponent of D is equal to thedegree of D.