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Étale duality of semistable schemes over local rings of positive characteristic

Zhao, Yigeng (2016) Étale duality of semistable schemes over local rings of positive characteristic. PhD, Universität Regensburg.

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Date of publication of this fulltext: 24 May 2016 11:48

Abstract (English)

In this thesis, we study duality theorems for the relative logarithmic de Rham-Witt sheaves on semi-stable schemes $X$ over a local ring $\mathbb{F}_q[[t]]$, for a finite field $\mathbb{F}_q$. As an application, we obtain a new filtration on the maximal abelian quotient $\pi^{\text{ab}}_1(U)$ of the \'etale fundamental groups $\pi_1(U)$ of an open subscheme $U \subseteq X$, which gives a measure ...

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Translation of the abstract (German)

In dieser Dissertation studieren wir Dualitätssatze für relative logarithmische de Rham-Witt Garben auf semi-stabilen Schemata über einem lokalen Ring $\mathbb{F}_q[[t]]$, wobei $\mathbb{F}_q$ ein endlicher Körper ist. Als Anwendung erhalten wir eine neue Filtrierung auf dem maximalen abelschen Quotienten $\pi^{\text{ab}}_1(U)$ der \'etalen Fundamentalgruppe auf einem offenen Unterschema $U ...

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Item type:Thesis of the University of Regensburg (PhD)
Date:24 May 2016
Referee:Prof. Dr. Uwe Jannsen
Date of exam:28 April 2016
Institutions:Mathematics > Prof. Dr. Uwe Jannsen
Classification:
NotationType
14F20MSC
14F35MSC
11R37MSC
14G17MSC
Keywords:Étale duality, relative logarithmic de Rham-Witt sheaves, purity, semi-stable schemes, ramification, class field theory.
Dewey Decimal Classification:500 Science > 510 Mathematics
Status:Published
Refereed:Yes, this version has been refereed
Created at the University of Regensburg:Yes
Item ID:33788
Owner only: item control page

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