The K(π,1)-property for marked curves over finite fields

Philippe Lebacque (1) , Alexander Schmidt (2)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
2 Mathematisches Institut

We investigate the K(π,1)-property for p of smooth, marked curves (X,T) defined over finite fields of characteristic p. We prove that (X,T) has the K(π,1)-property if X is affine and give positive and negative examples in the proper case. We also consider the unmarked proper case over a finite field of characteristic different to p.

Mots clés: Galois cohomology; étale cohomology; restricted ramification

Domaines: Théorie des nombres [math.NT]; Géométrie algébrique [math.AG]

Philippe Lebacque, Alexander Schmidt. The K(π,1)-property for marked curves over finite fields. 2013. ⟨hal-00926253v2⟩