Geodesic
Duality for Relative Logarithmic de Rham-Witt Sheaves on Semistable Schemes over $\mathbb F_q[[t]]$
Documenta mathematica, Tome 23 (2018), pp. 1925-1967.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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 $\pi^{{ab}}_1(U)$ 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 ${Supp}(D) \subseteq X-U$. This filtration coincides with the Brylinski-Kato-Matsuda filtration in the relative dimension zero case.
Classification : 14F20, 14F35, 11R37, 14G17
Keywords: logarithmic de Rham-Witt sheaf, purity, étale duality, étale fundamental group, semistable scheme, ramification, filtration, class field theory 
@article{DOCMA_2018__23__a8,
     author = {Zhao, Yigeng},
     title = {Duality for {Relative} {Logarithmic} de {Rham-Witt} {Sheaves} on {Semistable} {Schemes} over $\mathbb F_q[[t]]$},
     journal = {Documenta mathematica},
     pages = {1925--1967},
     publisher = {mathdoc},
     volume = {23},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2018__23__a8/}
}
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Zhao, Yigeng. Duality for Relative Logarithmic de Rham-Witt Sheaves on Semistable Schemes over $\mathbb F_q[[t]]$. Documenta mathematica, Tome 23 (2018), pp. 1925-1967. http://geodesic.mathdoc.fr/item/DOCMA_2018__23__a8/