Let $X=Spec\ A$ be a normal affine variety of dimension $n$ over an algebraically closed field $k$ of characteristic $p>0$. Also, assume that $S\subset X$ be a prime Weil-divisor on $X$. Now, I need to construct a birational model $g:Y\to X$ such that $Y$ and the birational transform $S'$ of $S$ are both normal and $g$ is a projective morphism ( or proper ).
Since we don't have the Resolution of Singularities in characteristic $p>0$, so I don't really know a good (or standard) way of doing this in higher dimension (n>3).
Any help will be greatly appreciated.