Anabelian geometry with etale homotopy types

• 成果类型: Article
• 署名作者: Schmidt, Alexander; Stix, Jakob
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2016.184.3.5
• 发表日期: 2016
• 页码: 817-868
• 关键词: grothendieck conjecture

摘要

Anabelian geometry with etale homotopy types generalizes in a natural way classical anabelian geometry with (tale 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 Q has a fundamental system of (affine) anabelian Zariski-neighborhoods. This was predicted by Grothendieck in his letter to Faltings.