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arXiv · 1611.08720

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

Uwe Jannsen·Shuji Saito·Yigeng Zhao
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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 wild ramification class field theory for the open subvariety $U$.

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Uwe Jannsen, Shuji Saito, Yigeng Zhao. 2017-10-16. Duality for relative logarithmic de Rham-Witt sheaves and wildly ramified class field theory over finite fields. https://doi.org/10.1112/s0010437x1800711x

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