O Teorema de Abel

Abstract

The purpose of this note is to present a proof of Abel's Theorem. Considering X be a compact Riemann surface, every principal divisor in X is a zero degree divisor. Therefore, naturally arises the following question: when a zero degree divisor is a principal divisor in X? Abel's Theorem answers this question, and stablish that if D is a zero degree divisor then D is a principal divisor of X if and only if A_0(D) = 0 on the Jacobian of X, where A0 is the map of Abel-Jacobi restricted to zero degree divisors.