Duality for relative logarithmic de Rham–Witt sheaves and wildly ramified class field theory over finite fields. (7th May 2018) - Jannsen, Uwe; Saito, Shuji; Zhao, Yigeng
Abstract : 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 $U$ .