Geodesic
The $K(\pi,1)$-property for smooth marked curves over finite fields
Izvestiya. Mathematics , Tome 79 (2015) no. 5, pp. 1043-1050

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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. 
@article{IM2_2015_79_5_a6,
     author = {Ph. Lebacque and A. Schmidt},
     title = {The $K(\pi,1)$-property for smooth marked curves over finite fields},
     journal = {Izvestiya. Mathematics },
     pages = {1043--1050},
     publisher = {mathdoc},
     volume = {79},
     number = {5},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2015_79_5_a6/}
}
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Ph. Lebacque; A. Schmidt. The $K(\pi,1)$-property for smooth marked curves over finite fields. Izvestiya. Mathematics , Tome 79 (2015) no. 5, pp. 1043-1050. http://geodesic.mathdoc.fr/item/IM2_2015_79_5_a6/