Abhyankar's affine arithmetic conjecture for the symmetric and alternating groups

DOI10.1016/j.jpaa.2023.107561arXiv2205.03879OpenAlexW4388075725MaRDI QIDQ6146480

Unnamed Author, Alexei Entin

Publication date: 5 February 2024

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2205.03879

zbMATH Keywords

function fieldsGalois theoryramification

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Galois theory (11R32) Inverse Galois theory (12F12)

Cites Work

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• Alternating group coverings of the affine line for characteristic greater than two
• Coverings of the affine line in characteristic \(p>0\) and Abhyankar's conjecture
• Abhyankar's conjecture on Galois groups over curves
• Small degree coverings of the affine line in characteristic two
• Alternating group coverings of the affine line for characteristic two
• Nice equations for nice groups
• Resolution of singularities and modular Galois theory
• Galois groups of some vectorial polynomials
• Coverings of Algebraic Curves
• Algebraic Function Fields and Codes
• The strong primitive normal basis theorem
• Galois theory on the line in nonzero characteristic
• Semilinear transformations
• Once more nice equations for nice groups
• Primitive free quartics with specified norm and trace
• Mixed exponential sums over finite fields
• Again nice equations for nice groups
• More nice equations for nice groups
• Primitive free cubics with specified norm and trace
• Further Nice Equations for Nice Groups
• Abhyankar’s conjectures in Galois theory: Current status and future directions
• PRIMITIVE PERMUTATION GROUPS CONTAINING A CYCLE

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