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Graded quaternion symbol equivalence of function fields

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Abstract

We present criteria for a pair of maps to constitute a quaternion-symbol equivalence (or a Hilbert-symbol equivalence if we deal with global function fields) expressed in terms of vanishing of the Clifford invariant. In principle, we prove that a local condition of a quaternion-symbol equivalence can be transcribed from the Brauer group to the Brauer-Wall group.

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References

  1. A. Czogała: Równoważność Hilberta ciał globalnych. Volume 1969 of Prace Naukowe Uniwersytetu Ślaskiego w Katowicach [Scientific Publications of the University of Silesia]. Wydawnictwo Uniwersytetu Ślaskiego, Katowice, 2001.

    Google Scholar 

  2. M. Knebusch: On algebraic curves over real closed fields. II. Math. Z. 151 (1976), 189–205.

    Article  MATH  MathSciNet  Google Scholar 

  3. P. Koprowski: Local-global principle for Witt equivalence of function fields over global fields. Colloq. Math. 91 (2002), 293–302.

    Article  MATH  MathSciNet  Google Scholar 

  4. P. Koprowski: Witt equivalence of algebraic function fields over real closed fields. Math. Z. 242 (2002), 323–345.

    Article  MATH  MathSciNet  Google Scholar 

  5. P. Koprowski: Integral equivalence of real algebraic function fields. Tatra Mt. Math. Publ. 32 (2005), 53–61.

    MATH  MathSciNet  Google Scholar 

  6. T. Y. Lam: Introduction to quadratic forms over fields. Volume 67 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI, 2005.

    Google Scholar 

  7. R. Perlis, K. Szymiczek, P. E. Conner and R. Litherland: Matching Witts with global fields. In Recent advances in real algebraic geometry and quadratic forms (Berkeley, CA, 1990/1991; San Francisco, CA, 1991), volume 155 of Contemp. Math., pages 365–387. Amer. Math. Soc., Providence, RI, 1994.

    Google Scholar 

  8. K. Szymiczek: Matching Witts locally and globally. Math. Slovaca 41 (1991), 315–330.

    MATH  MathSciNet  Google Scholar 

  9. K. Szymiczek: Witt equivalence of global fields. Comm. Algebra 19 (1991), 1125–1149.

    Article  MATH  MathSciNet  Google Scholar 

  10. K. Szymiczek: Hilbert-symbol equivalence of number fields. Tatra Mt. Math. Publ. 11 (1997), 7–16.

    MATH  MathSciNet  Google Scholar 

  11. K. Szymiczek: A characterization of tame Hilbert-symbol equivalence. Acta Math. Inform. Univ. Ostraviensis 6 (1998), 191–201.

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Instytut Matematyki, Uniwersytet Ślaski, ul. Bankowa 14, PL-40-007, Katowice, Poland

    Przemysław Koprowski

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  1. Przemysław Koprowski
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Correspondence to Przemysław Koprowski.

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Koprowski, P. Graded quaternion symbol equivalence of function fields. Czech Math J 57, 1311–1319 (2007). https://doi.org/10.1007/s10587-007-0125-x

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  • DOI: https://doi.org/10.1007/s10587-007-0125-x

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