Alexander Schmidt, Jakob Stix: Anabelian geometry with étale homotopy types

       Authors: Alexander Schmidt, Jakob Stix
       Title: Anabelian geometry with étale homotopy types
       in: Annals of Math. 184 (2016), Issue 3, 817-868

	Abstract: Anabelian geometry with étale homotopy types generalizes in a natural way classical anabelian geometry with étale fundamental groups. We show that, both in the classical and the generalized sense, any point of a smooth variety over a field k which is finitely generated over Q has a fundamental system of (affine) anabelian Zariski-neighbourhoods. This was predicted by Grothendieck in his letter to Faltings from 1983.

Abstract: Anabelian geometry with étale homotopy types generalizes in a natural way classical anabelian geometry with étale fundamental groups. We show that, both in the classical and the generalized sense, any point of a smooth variety over a field k which is finitely generated over Q has a fundamental system of (affine) anabelian Zariski-neighbourhoods. This was predicted by Grothendieck in his letter to Faltings from 1983.

pdf-file anab-hotype.pdf.

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