2023/02/27 by Olivier Wittenberg, Wittenberg, Olivier · 1 citation
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #History and Theory of Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2302.13719
openalex publication_date 2023/02/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
The inverse Galois problem asks whether any finite group can be realised as the Galois group of a Galois extension of the rationals. This problem and its refinements have stimulated a large amount of research in number theory and algebraic geometry in the past century, ranging from Noether's problem (letting X denote the quotient of the affine space by a finite group acting linearly, when is X rational?) to the rigidity method (if X is not rational, does it at least contain interesting rational curves?) and to the arithmetic of unirational varieties (if all else fails, does X at least contain interesting rational points?). The goal of the present notes, which formed the basis for three lectures given at the Park City Mathematics Institute in August 2022, is to provide an introduction to these topics.