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arXiv · 1504.01068

Anabelian geometry with etale homotopy types

Alexander Schmidt·Jakob Stix
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Abstract

Anabelian geometry with etale homotopy types generalizes in a natural way classical anabelian geometry with etale 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.

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Alexander Schmidt, Jakob Stix. 2016-07-12. Anabelian geometry with etale homotopy types. https://doi.org/10.4007/annals.2016.184.3.5

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