Division Algebras that Ramify only on a Plane Quartic Curve with Simply Connected Components

摘要

A central division algebra Λ over the field of rational functions in two variables with coefficients over an algebraically closed field ramifies along a divisor on P~2. If the ramification divisor of Λ is a quartic curve which is the union of simply connected curves, we show that Λ is a symbol algebra and satisfies the 'index equals exponent' equation.