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Généralités

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Book cover Groupes algébriques semi-simples en dimension cohomologique ≤2

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2238))

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Abstract

Ce premier chapitre se propose de rappeler les notions principales utilisées dans ce livre.

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Notes

  1. 1.

    On devrait parler en toute correctitude de K-algèbre d’Azumaya.

  2. 2.

    Attention, la référence [6] utilise un sens plus faible pour la notion de groupes métacyclique, c’est-à-dire extension de groupes finis cycliques.

  3. 3.

    Noter que la relation est triviale si k est le corps à deux éléments.

References

  1. M. Aschbacher, Finite Group Theory. Cambridge Studies in Advanced Mathematics, vol. 10 (Cambridge University Press, Cambridge, 1986)

    Google Scholar 

  2. G. Berhuy, C. Frings, J.-P. Tignol, Galois cohomology of the classical groups over imperfect fields. J. Pure Appl. Algebra 211, 307–341 (2007)

    Article  MathSciNet  Google Scholar 

  3. S. Bosch, W. Lütkebohmert, M. Raynaud, Néron Models (Springer, Berlin, 1990)

    Book  Google Scholar 

  4. J.-L. Colliot-Thélène, J.-J. Sansuc, La R-équivalence sur les tores. Ann. Sci. Éc. Norm. Supér. 10, 175–229 (1977)

    Article  Google Scholar 

  5. J.-L. Colliot-Thélène, J.-J. Sansuc, Principal homogeneous spaces under flasque tori: applications. J. Algebra 106, 148–205 (1987)

    Article  MathSciNet  Google Scholar 

  6. J.-L. Colliot-Thélène, J.-J. Sansuc, La descente sur les variétés rationnelles. Duke Math. J. 54, 375–492 (1987)

    Article  MathSciNet  Google Scholar 

  7. B. Conrad, O. Gabber, G. Prasad, Pseudo-Reductive Groups, 2nd edn. (Cambridge University Press, Cambridge, 2015)

    Book  Google Scholar 

  8. M. Demazure, P. Gabriel, Groupes algébriques (North-Holland, Amsterdam, 1970)

    MATH  Google Scholar 

  9. P. Gille, La R-équivalence sur les groupes algébriques réductifs définis sur un corps global. Publ. Math. l’I.H.É.S. 86, 199–235 (1997)

    Article  Google Scholar 

  10. P. Gille, Questions de rationalité sur les groupes algébriques linéaires, http://math.univ-lyon1.fr/homes-www/gille/prenotes/qrs2011.pdf

  11. P. Gille, A. Pianzola, Torsors, reductive group schemes and extended affine Lie algebras. Mem. Am. Math. Soc. 226(1063) (2013), 112 pp.

    Article  MathSciNet  Google Scholar 

  12. P. Gille, T. Szamuely, Central Simple Algebras and Galois Cohomology. Cambridge Studies in Advanced Mathematics, vol. 165, 2nd edn. (Cambridge University Press, Cambridge, 2017)

    Google Scholar 

  13. M-A. Knus, A. Merkurjev, M. Rost, J-P. Tignol, The Book of Involutions. AMS Colloquium Publications, vol. 44 (American Mathematical Society, Providence, 1998)

    Google Scholar 

  14. T.Y. Lam, Introduction to Quadratic Forms Over Fields. Graduate Studies in Mathematics, vol. 67 (American Mathematical Society, Providence, 2005)

    Google Scholar 

  15. T.Y. Lam, D.B. Leep, J.-P. Tignol, Biquaternion algebras and quartic extensions. Inst. Hautes Études Sci. Publ. Math. 77, 63–102 (1993)

    Article  MathSciNet  Google Scholar 

  16. Y.I. Manin, Cubic Forms. Algebra, Geometry, Arithmetic. North-Holland Mathematical Library, vol. 4, 2nd edn. (North-Holland, Amsterdam, 1986)

    Google Scholar 

  17. B. Margaux, Passage to the limit in non-abelian Čech cohomology. J. Lie Theory 17, 591–596 (2007)

    MathSciNet  MATH  Google Scholar 

  18. B. Margaux, The structure of the group G(k[t]): variations on a theme of Soulé. Algebra Number Theory 3, 393–409 (2009)

    Article  MathSciNet  Google Scholar 

  19. J. Milne, Étale Cohomology (Princeton University Press, Princeton, 1980)

    MATH  Google Scholar 

  20. J. Oesterlé, Nombres de Tamagawa et groupes unipotents en caractéristique p > 0. Inv. Math. 78, 13–88 (1984)

    Article  Google Scholar 

  21. M. Rosenlicht, Toroidal algebraic group. Proc. Am. Math. Soc. 12, 984–988 (1961)

    Article  MathSciNet  Google Scholar 

  22. J.-J. Sansuc, Groupe de Brauer et arithmétique des groupes algébriques linéaires sur un corps de nombres. J. Reine Angew. Math. 327, 12–80 (1981)

    MathSciNet  MATH  Google Scholar 

  23. L.L. Scott, Integral equivalence of permutation representations, in Group Theory (Granville, OH, 1992) (World Scientific, River Edge, 1993), pp. 262–274

    Google Scholar 

  24. J.-P. Serre, Cohomologie galoisienne, cinquième édition (Springer, New York, 1997)

    Google Scholar 

  25. S. Shatz, Profinite Groups, Arithmetic, and Geometry. Annals of Mathematics Studies (Princeton University Press, Princeton, 1972)

    MATH  Google Scholar 

  26. The Stacks Project, https://stacks.math.columbia.edu/

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Authors and Affiliations

  1. Camille Jordan Institute, CNRS, Université Lyon 1, Villeurbanne, France

    Philippe Gille

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  1. Philippe Gille
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Gille, P. (2019). Généralités. In: Groupes algébriques semi-simples en dimension cohomologique ≤2 . Lecture Notes in Mathematics, vol 2238. Springer, Cham. https://doi.org/10.1007/978-3-030-17272-5_1

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