Support of a Weil divisor ($\mathrm{Supp}(D)={\bigcup }_{a_P\ne 0}P$)

For $D={\sum }_P{a}_{P}P$, its support is the union of the prime divisors $P$ with $a_P\ne 0$. Negative as well as positive coefficients contribute. A point outside the support has a neighbourhood on which the divisor is zero.