0 Notations

where $(s_1,U_1)\sim (s_2,U_2)$ if there exists $W\subseteq U_1\cap U_2$ such that $x\in W$ and $s_1{|}_W=s_2{|}_W$.

Link to original

All the ${\underline{o}}_X(U)$ are subrings of $K(R)$. If $V\subset U$, then ${\underline{o}}_X(U)\subset {\underline{o}}_X(V)$; if we take the inclusion as the restriction map, this defines a sheaf ${\underline{o}}_X$.

Link to original