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Duality for relative logarithmic de Rham–Witt sheaves and wildly ramified class field theory over finite fields
- Part of
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- Journal:
- Compositio Mathematica / Volume 154 / Issue 6 / June 2018
- Published online by Cambridge University Press:
- 07 May 2018, pp. 1306-1331
- Print publication:
- June 2018
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- Article
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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 
$U$.
