Duality for relative logarithmic de Rham–Witt sheaves and wildly ramified class field theory over finite fields

In order to study$p$-adic étale 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 wildly ramified class field theory for the open subvariety$U$.