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Izvestiya: Mathematics, 2015, Volume 79, Issue 5, Pages 1043–1050
DOI: https://doi.org/10.1070/IM2015v079n05ABEH002770 (Mi im8282) 		 
The $K(\pi,1)$-property for smooth marked curves over finite fields

Ph. Lebacquea, A. Schmidtb

a Laboratoire de Mathématiques, Université de Franche-Comté, Besançon
b Universität Heidelberg, Mathematisches Institut
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DOI: https://doi.org/10.1070/IM2015v079n05ABEH002770
Abstract: In the case of smooth marked curves $(X,T)$ over finite fields of characteristic $p$, we study the $K(\pi,1)$-property for $p$. We prove that $(X,T)$ has the $K(\pi,1)$-property if $X$ is affine, and give positive and negative examples in the case when $X$ is proper. We also consider the case of unmarked proper curves over a finite field of characteristic different from $p$.
Keywords: Galois cohomology, étale cohomology, restricted ramification.
Received: 24.07.2014
Revised: 13.01.2015
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2015, Volume 79, Issue 5, Pages 193–200
DOI: https://doi.org/10.4213/im8282
Bibliographic databases:
Document Type: Article
UDC: 511.236+511.238.2+512.737
MSC: 11R34, 11R37, 14F20
Language: English
Original paper language: Russian
Citation: Ph. Lebacque, A. Schmidt, “The $K(\pi,1)$-property for smooth marked curves over finite fields”, Izv. Math., 79:5 (2015), 1043–1050
Citation in format AMSBIB
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\by Ph.~Lebacque, A.~Schmidt
\paper The $K(\pi,1)$-property for smooth marked curves over finite fields
\jour Izv. Math.
\yr 2015
\vol 79
\issue 5
\pages 1043--1050
\mathnet{http://mi.mathnet.ru//eng/im8282}
\crossref{https://doi.org/10.1070/IM2015v079n05ABEH002770}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84948402980}
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Russian version PDF:116
    English version PDF:6
    References:43
    First page:16
     
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