Elsevier

Journal of Algebra

Volume 508, 15 August 2018, Pages 364-389
Journal of Algebra

Cohomology of the geometric fundamental group of hyperbolic polycurves

https://doi.org/10.1016/j.jalgebra.2018.04.028Get rights and content
Under an Elsevier user license
open archive

Abstract

In the present paper, we study the cohomology groups of profinite groups obtained by successive extensions of families of (pro-Σ) surface groups. As an application, we show, among others, that the dimension of a hyperbolic polycurve (i.e., a successive extension of a family of hyperbolic curves) over a field of characteristic zero can be reconstructed group-theoretically from its geometric fundamental group.

MSC

20J06
14H30

Keywords

Profinite group cohomology
Étale fundamental group
Hyperbolic polycurve
Anabelian geometry

Cited by (0)