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

  • Uwe Jannsen (a1), Shuji Saito (a2) and Yigeng Zhao (a3)

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 $U$ .

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

  • Uwe Jannsen (a1), Shuji Saito (a2) and Yigeng Zhao (a3)

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