Remarks on the inverse Galois problem over function fields

DOI10.1016/j.ffa.2023.102343arXiv2211.15835OpenAlexW4388960879MaRDI QIDQ6185651

Shiang Tang

Publication date: 8 January 2024

Published in: Finite Fields and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2211.15835

zbMATH Keywords

global function fieldinverse Galois problemGalois representationscompatible systems

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Galois theory (11R32) Inverse Galois theory (12F12) Galois representations (11F80)

Cites Work

• Unnamed Item
• Coverings of the affine line in characteristic \(p>0\) and Abhyankar's conjecture
• Abhyankar's conjecture on Galois groups over curves
• Drinfeld shtukas and Langlands correspondence.
• Maximality of Galois actions for compatible systems
• Motivic Galois representations valued in spin groups
• Relative deformation theory, relative Selmer groups, and lifting irreducible Galois representations
• Potential automorphy of \(\mathrm{GSpin}_{2n+1}\)-valued Galois representations
• Lifting and automorphy of reducible mod \(p\) Galois representations over global fields
• \(\hat{G}\)-local systems on smooth projective curves are potentially automorphic
• Potential automorphy and change of weight
• Motives with exceptional Galois groups and the inverse Galois problem
• Functoriality and the inverse Galois problem
• COMPATIBLE SYSTEMS OF GALOIS REPRESENTATIONS ASSOCIATED TO THE EXCEPTIONAL GROUP
• Inverse Galois Theory
• Abhyankar’s conjectures in Galois theory: Current status and future directions

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