Étale Galois covers of affine smooth curves. The geometric case of a conjecture of Shafarevich. On Abhyankar's conjecture

DOI10.1007/BF01241142zbMath0842.14017OpenAlexW2913824484WikidataQ123130477 ScholiaQ123130477MaRDI QIDQ1895693

Florian Pop

Publication date: 25 July 1996

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/144288

zbMATH Keywords

function fieldfundamental groupabsolute Galois groupShafarevich conjectureAbhyankar's conjecturefinite split embedding problem

Mathematics Subject Classification ID

Galois theory (11R32) Coverings of curves, fundamental group (14H30) Galois cohomology (11R34)

Related Items (30)

A birational anabelian reconstruction theorem for curves over algebraically closed fields in arbitrary characteristic ⋮ Embedding problems for open subgroups of the fundamental group ⋮ The differential Galois group of the rational function field ⋮ The fundamental group of affine curves in positive characteristic ⋮ An embedding problem for finite local torsors over twisted curves ⋮ On the Hom-form of Grothendieck's birational anabelian conjecture in positive characteristic ⋮ Quasi-formations ⋮ Correction and addendum to ``Embedding problems with local conditions ⋮ Fundamental group in positive characteristic ⋮ Embedding problems and open subgroups ⋮ Monodromy groups of Kloosterman and hypergeometric sheaves ⋮ The Sylow subgroups of the absolute Galois group \(\mathrm{Gal}(\mathbb{Q})\) ⋮ LARGE FIELDS IN DIFFERENTIAL GALOIS THEORY ⋮ A refined version of Grothendieck's birational anabelian conjecture for curves over finite fields ⋮ Differential embedding problems over complex function fields ⋮ Simultaneous Surface Resolution in Cyclic Galois Extensions ⋮ Patching over fields ⋮ Permanence criteria for semi-free profinite groups. ⋮ Normal subgroups of the algebraic fundamental group of affine curves in positive characteristic ⋮ Fundamental groups of moduli and the Grothendieck-Teichmüller group ⋮ Abhyankar’s conjectures in Galois theory: Current status and future directions ⋮ Free differential Galois groups ⋮ Regular split embedding problems over function fields of one variable over ample fields ⋮ On function fields with free absolute Galois groups ⋮ Patching and thickening problems ⋮ Rigid local systems and finite symplectic groups ⋮ Embedding problems with local conditions ⋮ Subgroup Structure of Fundamental Groups in Positive Characteristic ⋮ Local systems and finite unitary and symplectic groups ⋮ Local Galois theory in dimension two

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