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 .