New York Journal of Mathematics
Volume 1 (1994-1995) 178-183


T. J. Ford

Division Algebras that Ramify Only Along a Singular Plane Cubic Curve

Published: September 18, 1995
Keywords: Brauer group, division algebra, central simple algebra, symbol algebra, cyclic algebra
Subject: Primary 13A20; Secondary 12E15, 14F20, 11R52

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

Author information

Department of Mathematics, Florida Atlantic University, Boca Raton, Florida 33431