  In order to study $p$-adic \'etale cohomology of an open subvariety $U$ of a
smooth proper variety $X$ over a perfect field of characteristic $p>0$, we
introduce new $p$-primary torsion sheaves. It is a modification of the
logarithmic de Rham-Witt sheaves of $X$ depending on effective divisors $D$
supported in $X-U$. Then we establish a perfect duality between cohomology
groups of the logarithmic de Rham-Witt cohomology of $U$ and an inverse limit
of those of the mentioned modified sheaves. Over a finite field, the duality
can be used to study wild ramification class field theory for the open
subvariety $U$.

Algebraic Geometry;Number Theory