2 problems

Let $A$ be a discrete valuation ring with local parameter $\pi$, perfect residue field $k$ of characteristic $p>0$, and fraction field $K$ of characteristic zero. Let…

Let $X$ be a smooth scheme over $S$ of dimension $d$. Write $X^{(a)}$ for the points of codimension $a$, $i_{*,x}$ for extension by zero from $x$, $\epsilon$ for the relevant morph…