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Brauer groups of rational function fields over global fields

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Groupe de Brauer

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References

  1. A.A. Albert, Structure of Algebras, Amer. Math. Soc. Coll. Publ. Vol. 24, Providence, R. I., 1961.

    Google Scholar 

  2. S.A. Amitsur, On central division algebras, Israel J. Math. 12 (1972), 408–420.

    Article  MathSciNet  MATH  Google Scholar 

  3. E. Artin and J. Tate, Class field theory, W.A. Benjamin, 1967.

    Google Scholar 

  4. M. Auslander and A. Brumer, Brauer groups of discrete valuation rings, Nederl. Akad. Wetensch. Proc. Ser A, 71 (1968), 286–296.

    Article  MathSciNet  MATH  Google Scholar 

  5. S. Bloch, Torsion algebraic cycles, K2, and the Brauer group of function fields, Bull. A.M.S. 80 (1974), 941–945.

    Article  MathSciNet  MATH  Google Scholar 

  6. J.W.S. Cassels and A. Fröhlich, Algebraic Number Theory, Thompson, Washington, 1967.

    MATH  Google Scholar 

  7. M. Deuring, Algebren, Springer-Verlag, New York, 1966.

    MATH  Google Scholar 

  8. D.K. Faddeev, Simple algebras over a field of algebraic functions of one variable, Trudy Mat. Inst. Steklov 38 (1951), 321–344; Amer. Math. Soc. Transl. Ser. II 3 (1956), 15–38.

    MathSciNet  Google Scholar 

  9. B. Fein and M. Schacher, Ulm invariants of the Brauer group of a field, Math. Z. 154 (1977), 41–50.

    Article  MathSciNet  MATH  Google Scholar 

  10. B. Fein and M. Schacher, Brauer groups and character groups of function fields, J. Algebra Vol. 61, No. 1, Nov. 1979, 249–255.

    Article  MathSciNet  MATH  Google Scholar 

  11. B. Fein, M. Schacher and J. Sonn, Brauer groups of rational function fields, Bull. A.M.S. (New Series) 1 (1979), 766–768.

    Article  MathSciNet  MATH  Google Scholar 

  12. E. Formanek, The center of the ring of 3 × 3 generic matrices, Lin. Mult. Alg. 7 (1979), 203–212.

    Article  MathSciNet  MATH  Google Scholar 

  13. E. Formanek, The center of the ring of 4 × 4 generic matrices, J. Alg. Vol. 62, No. 2 (1980), 304–320.

    Article  MathSciNet  MATH  Google Scholar 

  14. M. Greenberg, Lectures on Forms in Many Variables, Benjamin, New York, 1969.

    MATH  Google Scholar 

  15. K. Iwasawa, On Zl-extensions of algebraic number fields, Ann. of Math. 98 (1973) 187–326.

    Article  MathSciNet  Google Scholar 

  16. N. Jacobson, Lectures in Abstract Algebra, Vol. III, Van Nostrand, 1964.

    Google Scholar 

  17. J. Neukirch, Klassenkörpertheorie, B. I. Hochschulskripten, Mannheim, 1969.

    MATH  Google Scholar 

  18. C. Procesi, Rings with Polynomial Identities, Marcel Dekker, New York, 1973.

    MATH  Google Scholar 

  19. I. Reiner, Maximal Orders, Academic Press, New York, 1975.

    MATH  Google Scholar 

  20. J.-P. Serre, Cohomologie Galoisienne, Lecture Notes in Math. 9, Springer Verlag, Berlin, 1964.

    MATH  Google Scholar 

  21. J.-P. Serre, Corps Locaux, Hermann, Paris, 1962.

    MATH  Google Scholar 

  22. R. Snider, Is the Brauer group generated by cyclics? Lect. Notes in Math. 734 (Ring Theory, Waterloo 1978), Springer Verlag, Berlin, 1979.

    MATH  Google Scholar 

  23. J. Sonn, Class groups and Brauer groups, Israel J. Math., Vol. 34 Nos 1–2 (1979), 97–106.

    Article  MathSciNet  MATH  Google Scholar 

  24. J.P. Tignol, Sur les classes de similitude de corps à involution de degré 8, C.R. Acad. Sc. Paris 286 (1978), 875–876.

    MathSciNet  MATH  Google Scholar 

  25. E. Weiss, Algebraic Number Theory, New York, McGraw-Hill, 1963.

    MATH  Google Scholar 

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Authors

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Michel Kervaire Manuel Ojanguren

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© 1981 Springer-Verlag

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Fein, B., Schacher, M. (1981). Brauer groups of rational function fields over global fields. In: Kervaire, M., Ojanguren, M. (eds) Groupe de Brauer. Lecture Notes in Mathematics, vol 844. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090477

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  • DOI: https://doi.org/10.1007/BFb0090477

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10562-6

  • Online ISBN: 978-3-540-38531-8

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