Rational pullbacks of Galois covers

Arbarello, E., Cornalba, M.: Footnotes to a paper of Beniamino Segre: "On the modules of polygonal curves and on a complement to the Riemann existence theorem" (Italian) [Math. Ann. 100 (1928), 537-551

Jbuch 54, 685]. The number of $$g^{1}_{d}$$'s on a general $$d$$-gonal curve, and the unirationality of the Hurwitz spaces of $$4$$-gonal and $$5$$-gonal curves. Math. Ann., 256(3):341-362 (1981)

Bary-Soroker, L., Fehm, A.: Open problems in the theory of ample fields. In Geometric and differential Galois theories, volume 27 of Sémin. Congr., pages 1–11. Soc. Math. France, Paris (2013)

Dèbes, P., Deschamps, B.: The regular inverse Galois problem over large fields. In Geometric Galois actions, 2, volume 243 of London Math. Soc. Lecture Note Ser., pages 119–138. Cambridge Univ. Press, Cambridge (1997)

Dèbes, P., Douai, J-C.: Algebraic covers: field of moduli versus field of definition. Ann. Sci. École Norm. Sup. (4), 30(3):303–338 (1997)

Dèbes, P., König, J., Legrand, F., Neftin, D.: On parametric and generic polynomials with one parameter. J. Pure Appl. Algebra 225(10), 106717 (2021)

Dèbes, P., König, J., Legrand, F., Neftin, D.: Rational pullbacks of Galois covers. Manuscript (2018). arXiv:1807.01937v2

Dèbes, P.: Groups with no parametric Galois realizations. Ann. Sci. Éc. Norm. Supér. (4), 51(1):143–179 (2018)

Dèbes, P.: Méthodes topologiques et analytiques en théorie inverse de Galois : théorème d’existence de Riemann. (French). In Arithmétique de revêtements algébriques (Saint-Étienne, 2000), volume 5 of Sémin. Congr., pages 27–41. Soc. Math. France, Paris (2001)

Dèbes, P.: Density results for Hilbert subsets. Indian J. Pure Appl. Math. 30(1), 109–127 (1999)

Dèbes, P.: On the Malle conjecture and the self-twisted cover. Israel J. Math. 218(1), 101–131 (2017)

Dèbes, P., Legrand, F.: Specialization results in Galois theory. Trans. Am. Math. Soc. 365(10), 5259–5275 (2013)

Fried, M.D., Jarden, M.: Field arithmetic. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], 11. Springer-Verlag, Berlin, third edition, (2008). Revised by Jarden. xxiv+792 pp

Fried, M.D.: Fields of definition of function fields and Hurwitz families-groups as Galois groups. Comm. Algebra 5(1), 17–82 (1977)

Fried, M.D., Völklein, H.: The inverse Galois problem and rational points on moduli spaces. Math. Ann. 290(4), 771–800 (1991)

Grothendieck, A.: Eléments de géométrie algébrique. IV. Etude locale des schémas et des morphismes de schémas. I. (French). Inst. Hautes Etudes Sci. Publ. Math., 20, 259 pp (1964)

Jarden, M.: Algebraic patching. Springer Monographs in Mathematics. Springer, Heidelberg, 2011. xxiv+290 pp

Jensen, C.U., Ledet, A., Yui, N.: Generic polynomials. Constructive Aspects of the Inverse Galois Problem. Mathematical Sciences Research Institute Publications, 45. Cambridge University Press. x+258 pp (2002)

Jordan, C.: Recherches sur les substitutions. J. Liouville 17, 351–367 (1872)

König, J., Legrand, F.: Non-parametric sets of regular realizations over number fields. J. Algebra 497, 302–336 (2018)

König, J., Legrand, F., Neftin, D.: On the local behavior of specializations of function field extensions. Int. Math. Res. Not. IMRN 2019(9), 2951–2980 (2019)

Malle, G., Matzat, B.H.: Inverse Galois theory. Springer Monographs in Mathematics. Springer, Berlin. Second edition. xvii+532 pp (2018)

Müller, P.: Finiteness results for Hilbert’s irreducibility theorem. Ann. Inst. Fourier (Grenoble) 52(4), 983–1015 (2002)

Mumford, D.: The red book of varieties and schemes, volume 1358 of Lecture Notes in Mathematics. Springer-Verlag, Berlin, Second, expanded edition, 1999. Includes the Michigan lectures (1974) on curves and their Jacobians, With contributions by Enrico Arbarello. x+306 pp

Pop, F.: 1/2 Riemann existence theorem with Galois action. In Algebra and number theory (Essen, 1992), pages 193–218. de Gruyter, Berlin (1994)

Pop, F.: Embedding problems over large fields. Ann. Math. (2), 144(1):1–34 (1996)

Pop, F.: Little survey on large fields - old & new. In Valuation theory in interaction, EMS Ser. Congr. Rep., pages 432–463. Eur. Math. Soc., Zürich (2014)

Sadi, B.: Descente effective du corps de définition des revêtements. Thèse Université Lille 1, (1999). https://ori-nuxeo.univ-lille1.fr/nuxeo/site/esupversions/73ccb929-17bf-4a20-abc6-0aac9072c8d3

Silverman, J.H.: The arithmetic of elliptic curves, volume 106 of Graduate Texts in Mathematics. Springer, Dordrecht, second edition, (2009). xx+513 pp

Völklein, H.: Groups as Galois groups. An introduction, volume 53 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge, (1996). xviii+248 pp