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Algebraische Transformationsgruppen und Invariantentheorie Algebraic Transformation Groups and Invariant Theory pp 157–179Cite as

Birkhäuser

Fractions Rationnelles Invariantes par un Groupe Fini: Quelques Exemples

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Part of the book series: DMV Seminar ((OWS,volume 13))

Résumé

Il s’agit de la question classique (W. Burnside, E. Noether): soit G un groupe fini et V un G-module de dimension finie (sur le corps C des nombres complexes); on note C(V)G le corps des fonctions rationnelles sur V, invariantes par G; l’extension C(V)G/C est-elle transcendante pure?

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Bibliographie

  1. W. Barth, C. Peters, A. Van de Ven: Compact complex surfaces. Ergeb. Math. und Grenzgeb. 4, Springer-Verlag, Berlin Heidelberg New York 1984

    Google Scholar 

  2. A. Borel: Linear algebraic groups. W.A. Benjamin, Inc., New York 1969

    MATH  Google Scholar 

  3. N. Bourbaki: Algèbre, chapitre 5. Masson 1981

    Google Scholar 

  4. N. Bourbaki: Groupes et algèbres de Lie, chapitre 5. Hermann, Paris 1968

    MATH  Google Scholar 

  5. W. Burnside: Theory of groups of finite order, second edition. Cambridge University Press, Cambridge 1911

    MATH  Google Scholar 

  6. A. Cayley: A second memoir on quantics. Collected papers II, 250–275

    Google Scholar 

  7. J.-L. Colliot-Thélène, J.-J. Sansuc: Non rationalité de corps d’invariants sous un groupe fini (d’après Saltman et Bogomolov). Manuscript 1986

    Google Scholar 

  8. I. Dolgachev: Rationality of fields of invariants. In: Algebraic Geometry, Bowdoin 1985. Proc. Sympos. Pure Math. 46, part 2, 3–16

    Google Scholar 

  9. H. W. Lenstra jr.: Rational functions invariant under a finite abelian group. Invent. math. 25 (1974), 299–325

    Article  MathSciNet  MATH  Google Scholar 

  10. T. Miyata: Invariants of certain groups I; Nagoya Math. J. 41 (1971), 68–73

    MathSciNet  Google Scholar 

  11. E. Noether: Gleichungen mit vorgeschriebener Gruppe. Math. Ann. 78 (1916), 221–229

    Article  MathSciNet  Google Scholar 

  12. C. Procesi: Non commutative affine rings; Att. Acad. Naz. Lincei, Memoire 8 (1967), 237–255

    MathSciNet  Google Scholar 

  13. D. Saltman: Noether’s problem over an algebraically closed field. Invent. math. 77 (1984), 71–84

    Article  MathSciNet  MATH  Google Scholar 

  14. D. Saltman: Multiplicative field invariants. J. Algebra 106 (1987), 221–238

    Article  MathSciNet  MATH  Google Scholar 

  15. D. Saltman: Groups acting on fields: Noether’s problem. Contemp. math. 43 (1985), 267–277

    Article  MathSciNet  Google Scholar 

  16. J.-P. Serre: Corps locaux. Hermann, Paris 1962

    MATH  Google Scholar 

  17. J.-P. Serre: Critère de rationalité pour les surfaces algébriques. Sém. Bourbaki no. 146 (1957)

    Google Scholar 

  18. D. D. Triantaphyllou: Invariants of finite groups acting non-linearly on rational function fields. J. Pure Appl. Alg. 18 (1980), 315–331

    Article  MathSciNet  MATH  Google Scholar 

  19. E. B. Vinberg: Rationality of the field of invariants of a triangular group. Vestnik Mosk. Univ. Mat. 37 (1982), 23–24

    MathSciNet  Google Scholar 

  20. H. Weber: Lehrbuch der Algebra. Chelsea Publ. Comp., 1908

    Google Scholar 

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Authors
  1. Michel Kervaire
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  2. Thierry Vust
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Editor information

Editors and Affiliations

  1. Mathematisches Institut, Universität Basel, Rheinsprung 21, CH-4051, Basel, Schweiz

    Hanspeter Kraft

  2. Mathematisches Institut B, Universität Stuttgart, Paffenwaldring 57, D-7000, Stuttgart 80, Westdeutschland

    Peter Slodowy

  3. Mathematisch Instituut, Rijksuniversiteit, Budapestlaan 6, NL-3508 TA, Utrecht, Nederland

    Tonny A. Springer

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© 1989 Springer Basel AG

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Kervaire, M., Vust, T. (1989). Fractions Rationnelles Invariantes par un Groupe Fini: Quelques Exemples. In: Kraft, H., Slodowy, P., Springer, T.A. (eds) Algebraische Transformationsgruppen und Invariantentheorie Algebraic Transformation Groups and Invariant Theory. DMV Seminar, vol 13. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7662-9_10

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  • DOI: https://doi.org/10.1007/978-3-0348-7662-9_10

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-7663-6

  • Online ISBN: 978-3-0348-7662-9

  • eBook Packages: Springer Book Archive

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