Duality for relative logarithmic de Rham–Witt sheaves and wildly ramified class field theory over finite fields. (7th May 2018)

• Record Type: Journal Article
• Authors: Jannsen, Uwe; Saito, Shuji; Zhao, Yigeng
• Is Part Of: Compositio mathematica. Volume 154:Number 6(2018)
• Page Start: 1306
• Page End: 1331
• Publication Date: 2018-05-07
• Subjects: 14F20 (primary), -- 14F35, -- 11R37, -- 14G17 (secondary); logarithmic de Rham–Witt sheaves, -- class field theory, -- wild ramification, -- étale duality, -- quasi-algebraic groups; Mathematics -- Periodicals; 510
• DOI: 10.1112/S0010437X1800711X
• Languages: English
• ISSNs: 0010-437X

Abstract

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 $U$ .