Fundamental exact sequence for the pro-étale fundamental group

DOI10.2140/ant.2024.18.631arXiv1910.14015MaRDI QIDQ6122200

Marcin Lara

Publication date: 28 February 2024

Published in: Algebra \& Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1910.14015

zbMATH Keywords

étale fundamental grouphomotopy exact sequencepro-étale fundamental grouppro-étale topologyfundamental exact sequenceNoohi groups

Mathematics Subject Classification ID

Arithmetic ground fields (finite, local, global) and families or fibrations (14D10) Étale and other Grothendieck topologies and (co)homologies (14F20) Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations (20E06) Homotopy theory and fundamental groups in algebraic geometry (14F35)

Cites Work

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• Rational points and arithmetic of fundamental groups. Evidence for the section conjecture
• A general Seifert-van Kampen theorem for algebraic fundamental groups
• Fundamental groups of topological stacks with the slice property
• Specialization map between stratified bundles and pro-étale fundamental group
• Séminaire de géométrie algébrique du Bois Marie 1960/61 (SGA 1), dirigé par Alexander Grothendieck. Augmenté de deux exposés de M. Raynaud. Revêtements étales et groupe fondamental. Exposés I à XIII. (Seminar on algebraic geometry at Bois Marie 1960/61 (SGA 1), directed by Alexander Grothendieck. Enlarged by two reports of M. Raynaud. Ètale coverings and fundamental group)
• Submersions and effective descent of étale morphisms
• Homotopy Exact Sequence for the Pro-Étale Fundamental Group

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