I know we can define the linear system to a divisor. But how to define the linear system of an invertible sheaf. I meet this in the following context.
Let $X$ be a Noetherian scheme and $L$ be a line bundle on it. Then, the author talks about the linear system $|L|$.
I think the language of linear system is only defined for smooth projective $k$-varieties. But why could we use linear system in this case?
Is there any general corresponding between (class of) divisors and (class of) invertible sheaves on a scheme?
In general, could we define a linear system or a complete linear system for an invertible sheaf on a scheme?
