Solitons: Differential equations, symmetries, and infinite-dimensional algebras
《Solitons: Differential equations, symmetries, and infinite-dimensional algebras》 · 第 301 页 · Definition 11.20
A Cartier divisor $D$ on the integral scheme $X$ is given by a tuple $(U_i,f_i)$ where the $U_i$ form an open covering of $X$ and where $f_i\in K(X)^\times$ are elements with $f_if_j^{-1}\in\Gamma(U_i\cap U_j,\mathcal O_X^\times)$ for all $i,j$. Two tuples $(U_i,f_i)$, $(V_i,g_i)$ give rise to the same Cartier divisor, if $f_ig_j^{-1}\in\Gamma(U_i\cap V_j,\mathcal O_X^\times)$ for all $i,j$.