Skip to main content
SpringerLink
Log in

The inverse Galois problem and rational points on moduli spaces

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Ax, J.: The elementary theory of finite fields. Ann. Math.88, 239–271 (1968)

    Google Scholar 

  2. Biggers, R., Fried, M.: Moduli spaces of covers of ℙ1 and the Hurwitz monodromy group. J. Reine Angew. Math.335, 87–121 (1982)

    Google Scholar 

  3. Carter, R.: Simple groups of Lie type. (Pure Appl. Math., vol. 28) New York: Wiley 1972

    Google Scholar 

  4. Clebsch, A.: Zur Theorie der Riemann'schen Fläche. Math. Ann.6, 216–230 (1872)

    Google Scholar 

  5. Conway, J.H., Parker, R.A.: On the Hurwitz number of arrays of group elements, unpublished preprint, 1988

  6. Coombs, K., Harbater, D.: Hurwitz families and arithmetic Galois groups. Duke Math. J.52, 821–839 (1985)

    Google Scholar 

  7. Debes, P., Fried, M.: Regular extensions of ℝ(x) and Rigidity. Preprint

  8. Fried, M.: Fields of definition of function fields and Hurwitz families—groups as Galois groups. Commun. Algebra5, 17–82 (1977)

    Google Scholar 

  9. Fried, M.: Galois groups and complex multiplication. Trans. Am. Math. Soc.235, 141–162 (1978)

    Google Scholar 

  10. Fried, M.: Arithmetic of 3 and 4 branch point covers: a bridge provided by noncongruence subgroups of SL2(ℤ). Prog. Math.81, 77–117 (1989)

    Google Scholar 

  11. Fried, M., Jarden, M.: Field arithmetic. (Ergeb. Math. Grenzgeb., vol. 11) Berlin Heidelberg New York: Springer 1986

    Google Scholar 

  12. Fried, M., Jarden, M.: Diophantine properties of subfields of ℚ. Am. J. Math.100, 653–666 (1978)

    Google Scholar 

  13. Fried, M., Völklein, H.: The embedding problem over a Hilbertian PAC-field. Preprint

  14. Fulton, W.: Hurwitz schemes and irreducibility of moduli of algebraic curves. Ann. Math.90, 542–575 (1969)

    Google Scholar 

  15. Frey, G.: Pseudo-algebraically closed fields with non-archimedean real valuations. J. Algebra26, 202–207 (1973)

    Google Scholar 

  16. Huppert, B.: Endliche Gruppen I. (Grundl. Math. Wiss., vol. 134) Berlin Heidelberg New York: Springer 1967

    Google Scholar 

  17. Hurwitz, A.: Über Riemann'sche Flächen mit gegebenen Verzweigungspunkten. Math. Ann.39, 1–61 (1891)

    Google Scholar 

  18. Lubotzky, A., v. d. Dries, L.: Subgroups of free profinite groups and large subfields of ℚ. Isr. J. Math.39, 25–45 (1981)

    Google Scholar 

  19. Matzat, H.: Konstruktive Galoistheorie. (Lect. Notes Math., vol. 1284) Berlin Heidelberg New York: Springer 1986

    Google Scholar 

  20. Matzat, H.: Zöpfe und Galois'sche Gruppen. Preprint 1990

  21. Pop, F.: The totally real numbers are PRC. Preprint as of Oct. '90

  22. Serre, J.-P.: topics in Galois theory. Notes by H. Darmon. Harvard 1989

  23. Grothendieck, A.: Revêtements étale et groupes fondamental. (Lect. Notes Math., vol. 224) Berlin Heidelberg New York: Springer 1971

    Google Scholar 

  24. Thompson, J.G.: Some finite groups which occur as Gal(L/K) whereK≦ℚ(μ n ), J. Algebra89, 437–499 (1984)

    Google Scholar 

  25. Völklein, H.: PSL2(q) and extensions of ℚ(x). Bull. Am. Math. Soc.24, 145–153 (1991)

    Google Scholar 

  26. Weil, A.: The field of definition of a variety. Am. J. Math.78, 509–524 (1956)

    Google Scholar 

  27. Weissauer, R.: Der Hilbertsche Irreduzibilitätssatz. J. Reine Angew. Math.334, 203–220 (1982)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, UC Irvine, 92717, Irvine, CA, USA

    Michael D. Fried

  2. Department of Mathematics, University of Florida, 32611, Gainesville, FL, USA

    Helmut Völklein

  3. Universität Erlangen, W-8520, Erlangen, Germany

    Helmut Völklein

Authors
  1. Michael D. Fried
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Helmut Völklein
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Supported by NSF grant DMS-8702150 and BSF grant #87-00038

Supported by NSA grant MDA 904-89-H-2028

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fried, M.D., Völklein, H. The inverse Galois problem and rational points on moduli spaces. Math. Ann. 290, 771–800 (1991). https://doi.org/10.1007/BF01459271

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01459271

Keywords

Search

Navigation