Middle Convolution and Galois Realizations

  • Michael Dettweiler
Part of the Developments in Mathematics book series (DEVM, volume 11)


The theory of the middle convolution is combined with the theory of curves on Hurwitz spaces. This leads to the following theorem: The projective symplectic groups PSP 2n (Fp2) occur ℚ-regularly as Galois groups over ℚ(t) if p is an odd prime≢ ±1 mod 24.


Conjugacy Class Galois Group Homotopy Class Braid Group Jordan Block 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    J. S. Birman, “Braids, Links and Mapping Class Groups,” Princeton University Press, Princeton, 1974.Google Scholar
  2. [2]
    E. Bloch, “A First Course in Geometric Topology and Differential Geometry,” Birkhäuser, Boston, 1997.MATHGoogle Scholar
  3. [3]
    M. Dettweiler, Kurven auf Hurwitzräumen und ihre Anwendungen in der Galoistheorie, Dissertation, Erlangen, 1999.Google Scholar
  4. [4]
    M. Dettweiler, Plane curves and curves on Hurwitz spaces, IWR-Preprint (2001–06).Google Scholar
  5. [5]
    M. Dettweiler and S. Reiter, On rigid tuples in linear groups of odd dimension, J. Algebra 222 (1999), 550–560.MathSciNetMATHCrossRefGoogle Scholar
  6. [6]
    M. Dettweiler and S. Reiter, An algorithm of Katz and its application to the inverse Galois problem, J. Symb. Comp. 30 (2000), 761–798.MathSciNetMATHCrossRefGoogle Scholar
  7. [7]
    M. Dettweiler and S. Reiter, Monodromy of Puchsian systems, in preparation.Google Scholar
  8. [8]
    M. Dettweiler and S. Wewers, Hurwitz spaces and Shimura varieties, in preparation.Google Scholar
  9. [9]
    E. R. Fadell and S. Y. Husseini, “Geometry and Topology of Configuration Spaces,” Springer Verlag, Heidelberg, 2001.MATHCrossRefGoogle Scholar
  10. [10]
    M. Fried and H. Völklein, The inverse Galois problem and rational points on moduli spaces, Math. Ann. 290 (1991), 771–800.MathSciNetMATHCrossRefGoogle Scholar
  11. [11]
    N. Katz, “Rigid local systems,” Princeton University Press, Princeton, 1996.MATHGoogle Scholar
  12. [12]
    G. Malle and B. H. Matzat, “Inverse Galois theory,” Springer Verlag, Berlin, 1999.MATHGoogle Scholar
  13. [13]
    T. Shiina, Rigid braid orbits related to PSL2(p2) and some simple groups, preprint (2002).Google Scholar
  14. [14]
    T. Shiina, Regular Galois realizations of PSL2(p2) over Q(T), to appear in this volume.Google Scholar
  15. [15]
    H. Völklein, “Groups as Galois groups,” Cambridge Univ. Press, Cambridge, 1996.MATHCrossRefGoogle Scholar
  16. [16]
    H. Völklein, The braid group and linear rigidity, Geom. Dedicata 84 (2001), 135–150.MathSciNetMATHCrossRefGoogle Scholar
  17. [17]
    H. Völklein, A transformation principle for covers ofl, J. Reine Angew. Math. 534 (2001), 155–168.MATHCrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Michael Dettweiler
    • 1
  1. 1.IWR, Universität HeidelbergHeidelbergGermany

Personalised recommendations