Geodesic
Anabelian geometry with étale homotopy types
Alexander Schmidt 1   ; Jakob Stix 2
1 Mathematisches Institut, Universität Heidelberg, Heidelberg, Germany
2 Institut für Mathematik, Goethe--Universität Frankfurt, Frankfurt am Main, Germany
Annals of mathematics, Tome 184 (2016) no. 3, pp. 817-868 Cet article a éte moissonné depuis la source Annals of Mathematics website

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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 $k$ that is finitely generated over $\mathbb{Q}$ has a fundamental system of (affine) anabelian Zariski-neighborhoods. This was predicted by Grothendieck in his letter to Faltings.

DOI : 10.4007/annals.2016.184.3.5

Alexander Schmidt  1   ; Jakob Stix  2

1 Mathematisches Institut, Universität Heidelberg, Heidelberg, Germany
2 Institut für Mathematik, Goethe--Universität Frankfurt, Frankfurt am Main, Germany 
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Alexander Schmidt; Jakob Stix. Anabelian geometry with  étale homotopy types. Annals of mathematics, Tome 184 (2016) no. 3, pp. 817-868. doi: 10.4007/annals.2016.184.3.5

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