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Middle Convolution and Galois Realizations

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Galois Theory and Modular Forms

Part of the book series: Developments in Mathematics ((DEVM,volume 11))

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.

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References

  1. J. S. Birman, “Braids, Links and Mapping Class Groups,” Princeton University Press, Princeton, 1974.

    Google Scholar 

  2. E. Bloch, “A First Course in Geometric Topology and Differential Geometry,” Birkhäuser, Boston, 1997.

    MATH  Google Scholar 

  3. M. Dettweiler, Kurven auf Hurwitzräumen und ihre Anwendungen in der Galoistheorie, Dissertation, Erlangen, 1999.

    Google Scholar 

  4. M. Dettweiler, Plane curves and curves on Hurwitz spaces, IWR-Preprint (2001–06).

    Google Scholar 

  5. M. Dettweiler and S. Reiter, On rigid tuples in linear groups of odd dimension, J. Algebra 222 (1999), 550–560.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  7. M. Dettweiler and S. Reiter, Monodromy of Puchsian systems, in preparation.

    Google Scholar 

  8. M. Dettweiler and S. Wewers, Hurwitz spaces and Shimura varieties, in preparation.

    Google Scholar 

  9. E. R. Fadell and S. Y. Husseini, “Geometry and Topology of Configuration Spaces,” Springer Verlag, Heidelberg, 2001.

    Book  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  11. N. Katz, “Rigid local systems,” Princeton University Press, Princeton, 1996.

    MATH  Google Scholar 

  12. G. Malle and B. H. Matzat, “Inverse Galois theory,” Springer Verlag, Berlin, 1999.

    MATH  Google Scholar 

  13. T. Shiina, Rigid braid orbits related to PSL2(p2) and some simple groups, preprint (2002).

    Google Scholar 

  14. T. Shiina, Regular Galois realizations of PSL2(p2) over Q(T), to appear in this volume.

    Google Scholar 

  15. H. Völklein, “Groups as Galois groups,” Cambridge Univ. Press, Cambridge, 1996.

    Book  MATH  Google Scholar 

  16. H. Völklein, The braid group and linear rigidity, Geom. Dedicata 84 (2001), 135–150.

    Article  MathSciNet  MATH  Google Scholar 

  17. H. Völklein, A transformation principle for covers ofl, J. Reine Angew. Math. 534 (2001), 155–168.

    Article  MATH  Google Scholar 

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© 2004 Kluwer Academic Publishers

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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

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  • 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

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