The fundamental group of affine curves in positive characteristic

DOI10.1016/j.jalgebra.2013.10.007zbMath1329.14066arXiv0903.4472OpenAlexW2963218896MaRDI QIDQ397859

Manish Kumar

Publication date: 12 August 2014

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0903.4472

zbMATH Keywords

positive characteristicGalois theoryprofinite groupsetale covers of curves

Mathematics Subject Classification ID

Coverings of curves, fundamental group (14H30) Homotopy theory and fundamental groups in algebraic geometry (14F35)

Related Items (1)

Embedding problems for open subgroups of the fundamental group

Cites Work

• Fundamental group in positive characteristic
• Normal subgroups of the algebraic fundamental group of affine curves in positive characteristic
• Coverings of the affine line in characteristic \(p>0\) and Abhyankar's conjecture
• Abhyankar's conjecture on Galois groups over curves
• Étale Galois covers of affine smooth curves. The geometric case of a conjecture of Shafarevich. On Abhyankar's conjecture
• 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)
• Local Galois theory in dimension two
• Families of wildly ramified covers of curves
• On function fields with free absolute Galois groups
• Field Arithmetic
• Finiteness of isomorphism classes of curves in positive characteristic with prescribed fundamental groups
• The absolute Galois group of \(C(x)\)
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