Inverse Galois: source and evidence

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1 \renewcommand{\bibname}{Primary sources}
2 \begin{thebibliography}{9}
3 \addcontentsline{toc}{chapter}{Primary sources}
4 
5 \bibitem{Milne2022}
6 J. S. Milne.
7 \emph{Fields and Galois Theory}.
8 Kea Books, 2022.
9 Author-hosted edition, checked 9 October 2026.
10 \url{https://www.jmilne.org/math/Books/FT0.pdf}.
11 
12 \bibitem{SchmidtWingberg1998}
13 Alexander Schmidt and Kay Wingberg.
14 \emph{Safarevi\v{c}'s theorem on solvable groups as Galois groups}.
15 \texttt{arXiv:math/9809211v1}, 17 September 1998.
16 Theorem 1 gives the corrected solvable realization input.
17 \url{https://arxiv.org/abs/math/9809211v1}.
18 
19 \bibitem{DebesHarbater2021}
20 Pierre D\`ebes and David Harbater.
21 Pre-Galois theory.
22 \emph{Osaka Journal of Mathematics} \textbf{58} (2021), 71--101.
23 Published author-hosted copy.
24 \url{https://pro.univ-lille.fr/fileadmin/user_upload/pages_pros/pierre_debes/A59-DebesHarbater2.pdf}.
25 
26 \bibitem{DebesLectureNotes}
27 Pierre D\`ebes.
28 \emph{Arithm\'etique des rev\^etements de la droite}.
29 Author lecture manuscript, 385-page snapshot checked 9 October 2026.
30 The author publication page describes a 2024 work in progress.
31 Theorems 2.6.3 and 5.2.4 and Proposition 5.2.14 supply the specialization input.
32 \url{https://pro.univ-lille.fr/fileadmin/user_upload/pages_pros/pierre_debes/V2-ArithRevDte-v3.pdf.pdf}.
33 
34 \bibitem{Debes2026}
35 Pierre D\`ebes.
36 \emph{Hurwitz spaces and inverse Galois theory}.
37 Author manuscript dated 9 April 2026, 27 pages.
38 \url{https://pro.univ-lille.fr/fileadmin/user_upload/pages_pros/pierre_debes/A67-Nakamura60.pdf}.
39 
40 \bibitem{HuangEtAl2026}
41 Xiaoyu Huang, Blake Jackson, Kyu-Hwan Lee, Bjorn Poonen,
42 Rachel Pries and Shaowu Zhang.
43 \emph{The Mathieu group $M_{23}$ is a Galois group over $\mathbb Q$}.
44 \texttt{arXiv:2608.08538v2}, submitted 7 October 2026.
45 Manuscript dated 4 October 2026. Preprint used for dated context.
46 \url{https://arxiv.org/abs/2608.08538v2}.
47 
48 \bibitem{ConradCyclotomic}
49 Keith Conrad.
50 \emph{Cyclotomic Extensions}.
51 Undated author notes, snapshot checked 9 October 2026.
52 \url{https://kconrad.math.uconn.edu/blurbs/galoistheory/cyclotomic.pdf}.
53 
54 \bibitem{ConradPatternsPrimes}
55 Keith Conrad.
56 \emph{Patterns in Primes}.
57 Undated author notes, snapshot checked 9 October 2026.
58 Theorem 2.4 states the classical Dirichlet input.
59 \url{https://kconrad.math.uconn.edu/blurbs/ugradnumthy/prime-patterns-1.pdf}.
60 
61 \end{thebibliography}

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