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
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We study duality theorems for the relative logarithmic de Rham-Witt sheaves on semi-stable schemes X over a local ring Fq​[[t]], where Fq​ is a finite field. As an application, we obtain a new filtration on the maximal abelian quotient π1ab​(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.
DOI : 10.4171/dm/664
Classification : 11R37, 14F20, 14F35, 14G17
Mots-clés : class field theory, filtration, logarithmic de Rham-Witt sheaf, purity, étale duality, étale fundamental group, semistable scheme, ramification 
@article{10_4171_dm_664,
     author = {Yigeng Zhao},
     title = {Duality for {Relative} {Logarithmic} de {Rham-Witt} {Sheaves} on {Semistable} {Schemes} over $\mathbb F_q[[t]]$},
     journal = {Documenta mathematica},
     pages = {1925--1967},
     year = {2018},
     volume = {23},
     doi = {10.4171/dm/664},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/664/}
}
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Yigeng Zhao. Duality for Relative Logarithmic de Rham-Witt Sheaves on Semistable Schemes over $\mathbb F_q[[t]]$. Documenta mathematica, Tome 23 (2018), pp. 1925-1967. doi: 10.4171/dm/664

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