Application of generalized Weierstraß points: divisibilty of divisor classes (original) (raw)

This paper presents a direct algebraic proof of the divisibility of divisor classes of degree zero in the elliptic case, leveraging the properties of generalized Weierstraß points. The theory surrounding these points is reviewed before detailing their application in establishing the existence of certain local subrings, which are critical in the proof of the main result. The findings conclude that the divisor class group of elliptic function fields over algebraically closed fields of non-zero characteristic is indeed divisible.