Duality for relative logarithmic de Rham-Witt sheaves on semistable schemes over ${\mathbb{F}}_q[[t]]$

Abstract

We study duality theorems for the relative logarithmic de Rham-Witt sheaves on semi-stable schemes $X$ over a local ring ${\mathbb{F}}_q[[t]]$, where ${\mathbb{F}}_q$ is a finite field. As an application, we obtain a new filtration on the maximal abelian quotient ${\pi }_1^{\text{ab}}(U)$ of the étale fundamental groups ${\pi }_1(U)$ of an open subscheme $U\subseteq X$, which gives a measure of ramification along a divisor $D$ with normal crossing and $\text{Supp}(D)\subseteq X-U$. This filtration coincides with the Brylinski-Kato-Matsuda filtration in the relative dimension zero case.

final version

References in corpus (1)

• Higher Chow groups with modulus and relative Milnor K-theory

Cited by in corpus (1)

• Ramified class field theory and duality over finite fields