Abstract
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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
J. S. Birman, “Braids, Links and Mapping Class Groups,” Princeton University Press, Princeton, 1974.
E. Bloch, “A First Course in Geometric Topology and Differential Geometry,” Birkhäuser, Boston, 1997.
M. Dettweiler, Kurven auf Hurwitzräumen und ihre Anwendungen in der Galoistheorie, Dissertation, Erlangen, 1999.
M. Dettweiler, Plane curves and curves on Hurwitz spaces, IWR-Preprint (2001–06).
M. Dettweiler and S. Reiter, On rigid tuples in linear groups of odd dimension, J. Algebra 222 (1999), 550–560.
M. Dettweiler and S. Reiter, An algorithm of Katz and its application to the inverse Galois problem, J. Symb. Comp. 30 (2000), 761–798.
M. Dettweiler and S. Reiter, Monodromy of Puchsian systems, in preparation.
M. Dettweiler and S. Wewers, Hurwitz spaces and Shimura varieties, in preparation.
E. R. Fadell and S. Y. Husseini, “Geometry and Topology of Configuration Spaces,” Springer Verlag, Heidelberg, 2001.
M. Fried and H. Völklein, The inverse Galois problem and rational points on moduli spaces, Math. Ann. 290 (1991), 771–800.
N. Katz, “Rigid local systems,” Princeton University Press, Princeton, 1996.
G. Malle and B. H. Matzat, “Inverse Galois theory,” Springer Verlag, Berlin, 1999.
T. Shiina, Rigid braid orbits related to PSL2(p2) and some simple groups, preprint (2002).
T. Shiina, Regular Galois realizations of PSL2(p2) over Q(T), to appear in this volume.
H. Völklein, “Groups as Galois groups,” Cambridge Univ. Press, Cambridge, 1996.
H. Völklein, The braid group and linear rigidity, Geom. Dedicata 84 (2001), 135–150.
H. Völklein, A transformation principle for covers of ℙl, J. Reine Angew. Math. 534 (2001), 155–168.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Kluwer Academic Publishers
About this chapter
Cite this chapter
Dettweiler, M. (2004). Middle Convolution and Galois Realizations. In: Hashimoto, Ki., Miyake, K., Nakamura, H. (eds) Galois Theory and Modular Forms. Developments in Mathematics, vol 11. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0249-0_7
Download citation
DOI: https://doi.org/10.1007/978-1-4613-0249-0_7
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-7960-7
Online ISBN: 978-1-4613-0249-0
eBook Packages: Springer Book Archive