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

Author: Ford T. J.  

Publisher: Springer Publishing Company

ISSN: 1386-923X

Source: Algebras and Representation Theory, Vol.6, Iss.5, 2003-12, pp. : 501-514

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Abstract

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 P2. 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.