Duality for relative logarithmic de Rham-Witt sheaves on semistable schemes over \mathbbF_q[[t]]

2016/11/26 by Zhao, Yigeng
#11R37 #14F20 #14F35 #14G17 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1611.08722

Abstract

We study duality theorems for the relative logarithmic de Rham-Witt sheaves on semi-stable schemes X over a local ring \mathbbF_q[[t]], where \mathbbF_q is a finite field. As an application, we obtain a new filtration on the maximal abelian quotient π^ab₁(U) of the étale fundamental groups π₁(U) of an open subscheme U ⊆ X, which gives a measure of ramification along a divisor D with normal crossing and Supp(D) ⊆ X-U. This filtration coincides with the Brylinski-Kato-Matsuda filtration in the relative dimension zero case.

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