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I have my question on Q-Cartier Weil divisor. People say $D$ is Q-Cartier divisor if $nD$ is Cartier for some $n \geq 1$. Especially for $n > 1$, I have never seen the `rigorous' definition of $...

Let $f:X\to Y$ be a surjective morphism between two projective schemes over a field of characteristic $p>0$. Also assume that $X$ is smooth,$Y$ smooth & irreducible and $f_*\mathcal{O}_X=\...

Let $X$ be a normal scheme and $|D|$ a linear system on $X$. In "Singularity of Minimal Model Program" by Janos kollar p249, it says, If $X$ is a variety over $\mathbb{C}$, and $E_j$ ...