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Brauer group and diophantine geometry: A cohomological approach

Part of the Lecture Notes in Mathematics book series (LNM,volume 917)

Keywords

  • Exact Sequence
  • Galois Group
  • Pezzo Surface
  • Quaternion Algebra
  • Local Degree

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References

  1. B.J. Birch and H.P.F. Swinnerton-Dyer The Hasse problem for rational surfaces, J. reine angew. Math. 274 (1975), 164–174.

    MathSciNet  MATH  Google Scholar 

  2. J.W.S. Cassels and A. Frőhlich, Algebraic Number Theory, Thompson, Washington, 1967.

    MATH  Google Scholar 

  3. J.-L. Colliot-Thélène, D. Coray et J.-J. Sansuc, Descente et principe de Hasse pour certaines variétés rationnelles, J. reine angew. Math. 320 (1980), 150–191.

    MathSciNet  MATH  Google Scholar 

  4. S. Eilenberg and S. MacLane, Algebraic cohomology groups and loops, Duke Math. J. 14 (1947), 435–463.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. R. Hartshorne, Algebraic Geometry, Graduate Texts in Math. 52, Springer (1977).

    Google Scholar 

  6. V.A. Iskovskih, A counterexample to the Hasse principle for a system of two quadratic forms in five variables, Mat. Zametki 10 (1971), 253–257 (Transl.: Math. Notes 10 (1971), 575–577).

    MathSciNet  Google Scholar 

  7. Ju. I. Manin, Cubic forms: Algebra, Geometry, Arithmetic, North-Holland, Amsterdam (1974).

    MATH  Google Scholar 

  8. I. Reiner, Maximal orders, Academic Press, New-York (1975).

    MATH  Google Scholar 

  9. J. Tate, Homology of Noetherian rings and local rings, Illinois J. of Math. 1 (1957).

    Google Scholar 

  10. M.-F. Vignéras, Arithmétique des Algèbres de Quaternions, Lecture Notes in Math. 800 (1980).

    Google Scholar 

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© 1982 Springer-Verlag

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Hűrlimann, W. (1982). Brauer group and diophantine geometry: A cohomological approach. In: van Oystaeyen, F.M.J., Verschoren, A.H.M.J. (eds) Brauer Groups in Ring Theory and Algebraic Geometry. Lecture Notes in Mathematics, vol 917. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0092227

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  • DOI: https://doi.org/10.1007/BFb0092227

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11216-7

  • Online ISBN: 978-3-540-39057-2

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