On a scheme $X$ , a Cartier divisor is a global section of the sheaf $\mathcal{K}^*/\O^*$ , where $\mathcal{K}^*$ is the multiplicative sheaf of meromorphic functions, and $\O^*$ the multiplicative sheaf of invertible regular functions (the units of the structure sheaf).

More explicitly, a Cartier divisor is a choice of open cover $U_i$ of $X$ , and meromorphic functions $f_i\in \mathcal{K}^*(U_i)$ , such that $f_i/f_j\in\O^*(U_{i}\cap U_j)$ , along with two Cartier divisors being the same if the open cover of one is a refinement of the other, with the same functions attached to open sets, or if $f_i$ is replaced by $gf_i$ with $g\in\O_*$ .

Intuitively, the only information carried by Cartier divisor is where it vanishes, and the order it does there. Thus, a Cartier divisor should give us a Weil divisor, and vice versa. On ``nice'' (for example, nonsingular over an algebraically closed field) schemes, it does.