Weil divisor

Summary

A Weil divisor on a suitable scheme $X$ is a formal sum with integer coefficients of finitely many closed subvarieties of codimension one. The zeros and poles of a rational function, counted with multiplicity, form a principal Weil divisor. The quotient of all Weil divisors by the principal ones is the divisor class group, which equals the Picard group on smooth varieties.