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Rationality Criteria for Galois Extensions

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Galois Groups over ℚ

Part of the book series: Mathematical Sciences Research Institute Publications ((MSRI,volume 16))

Abstract

Some rationality criteria for finite Galois extensions overℂ(t)are explained. The first rationality criterion and the second rationality criterion, together with the corresponding examples are contained in the forthcoming lecture notes [27] (see also [23—25]). The rationality criteria in sections 4 and 5, the braid orbit theorem, and the twisted braid orbit theorem, are new. With the last one, the Mathieu group M24 is realized as Galois group over ℚ.

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Author information

Authors and Affiliations

  1. Mathematisches Institut II, Universität Karlsruhe (TH), Englerstraße 2, D-7500, Karlsruhe 1, Federal Republic of Germany

    B. Heinrich Matzat

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  1. B. Heinrich Matzat
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Editor information

Editors and Affiliations

  1. Faculty of Science, Department of Mathematics, Hongo, Tokyo 113, Japan

    Y. Ihara

  2. Department of Mathematics, University of California at Berkeley, 94720, Berkeley, CA, USA

    K. Ribet

  3. College de France, 3 Rue de Ulm, 75005, Paris, France

    J.-P. Serre

  4. Mathematical Sciences Research Institute, 1000 Centennial Drive, 94720, Berkeley, CA, USA

    K. Ribet

Additional information

Dedicated to my teacher Prof. H. W. Leopoldt on his 60th birthday

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© 1989 Springer-Verlag New York Inc.

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Matzat, B.H. (1989). Rationality Criteria for Galois Extensions. In: Ihara, Y., Ribet, K., Serre, JP. (eds) Galois Groups over ℚ. Mathematical Sciences Research Institute Publications, vol 16. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9649-9_6

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  • DOI: https://doi.org/10.1007/978-1-4613-9649-9_6

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4613-9651-2

  • Online ISBN: 978-1-4613-9649-9

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