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

Part of: Arithmetic problems. Diophantine geometry (Co)homology theory Algebraic number theory: global fields

Published online by Cambridge University Press:  07 May 2018

Uwe Jannsen ,
Shuji Saito  and
Yigeng Zhao
Uwe Jannsen
Affiliation:
Fakultät für Mathematik, Universität Regensburg, 93040 Regensburg, Germany email uwe.jannsen@mathematik.uni-regensburg.de
Shuji Saito
Affiliation:
Interactive Research Center of Science, Graduate School of Science and Engineering, Tokyo Institute of Technology, 2-12-1 Okayama, Meguro, Tokyo 152-8551, Japan email sshuji@msb.biglobe.ne.jp
Yigeng Zhao
Affiliation:
Fakultät für Mathematik, Universität Regensburg, 93040 Regensburg, Germany email yigeng.zhao@mathematik.uni-regensburg.de
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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 wildly ramified class field theory for the open subvariety $U$.

Keywords

logarithmic de Rham–Witt sheavesclass field theorywild ramificationétale dualityquasi-algebraic groups

MSC classification

Primary: 14F20: Étale and other Grothendieck topologies and (co)homologies
Secondary: 14F35: Homotopy theory; fundamental groups 11R37: Class field theory 14G17: Positive characteristic ground fields
Type
Research Article
Information
Compositio Mathematica , Volume 154 , Issue 6 , June 2018 , pp. 1306 - 1331
Copyright
© The Authors 2018 

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