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A remark on the structure of torsors under an affine group scheme

  • Christopher Deninger
Article
  • 71 Downloads

Abstract

It is well known that all torsors under an affine algebraic group over an algebraically closed field are trivial. We note that under suitable conditions this also holds if the group is not necessarily of finite type. This has an application to isomorphisms of fibre functors on neutral Tannakian categories.

Keywords

Torsor Algebraic group Tannakian category 

Mathematics Subject Classification

14L15 

References

  1. 1.
    Deligne, P., Milne, J.S.: Tannakian categories, Hodge Cycles, Motives, and Shimura Varieties, LNM 900, 1982, 101–228. An updated version is available under www.jmilne.org/math/
  2. 2.
    Hochschild, G., Mostow, G.D.: Representations and representative functions of Lie groups. Ann. Math. 2(66), 495–542 (1957)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Krull, Wolfgang: Jacobsonsche Ringe, Hilbertscher Nullstellensatz, Dimensionstheorie. Math. Z. 54, 354–387 (1951)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Lang, Serge: Hilbert’s Nullstellensatz in infinite-dimensional space. Proc. Am. Math. Soc. 3, 407–410 (1952)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Milnor, John W., Moore, John C.: On the structure of Hopf algebras. Ann. Math. 2(81), 211–264 (1965)CrossRefzbMATHGoogle Scholar
  6. 6.
    Waterhouse, William C.: An empty inverse limit. Proc. Am. Math. Soc. 36, 618 (1972)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Waterhouse, William C.: Introduction to Affine Group Schemes, Volume 66 of Graduate Texts in Mathematics. Springer, New York (1979)CrossRefGoogle Scholar

Copyright information

© The Author(s) 2017

Authors and Affiliations

  1. 1.MünsterGermany

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