Matching local Witt invariants

Przemysław Koprowski

Acta Mathematica Universitatis Ostraviensis (2005)

  • Volume: 13, Issue: 1, page 29-34
  • ISSN: 1804-1388

Abstract

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The starting point of this note is the observation that the local condition used in the notion of a Hilbert-symbol equivalence and a quaternion-symbol equivalence — once it is expressed in terms of the Witt invariant — admits a natural generalisation. In this paper we show that for global function fields as well as the formally real function fields over a real closed field all the resulting equivalences coincide.

How to cite

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Koprowski, Przemysław. "Matching local Witt invariants." Acta Mathematica Universitatis Ostraviensis 13.1 (2005): 29-34. <http://eudml.org/doc/35150>.

@article{Koprowski2005,
abstract = {The starting point of this note is the observation that the local condition used in the notion of a Hilbert-symbol equivalence and a quaternion-symbol equivalence — once it is expressed in terms of the Witt invariant — admits a natural generalisation. In this paper we show that for global function fields as well as the formally real function fields over a real closed field all the resulting equivalences coincide.},
author = {Koprowski, Przemysław},
journal = {Acta Mathematica Universitatis Ostraviensis},
keywords = {Witt invariant; Brauer group; Brauer-Wall group; Witt equivalence; Witt invariant; Brauer group; Brauer-Wall group; Witt equivalence},
language = {eng},
number = {1},
pages = {29-34},
publisher = {University of Ostrava},
title = {Matching local Witt invariants},
url = {http://eudml.org/doc/35150},
volume = {13},
year = {2005},
}

TY - JOUR
AU - Koprowski, Przemysław
TI - Matching local Witt invariants
JO - Acta Mathematica Universitatis Ostraviensis
PY - 2005
PB - University of Ostrava
VL - 13
IS - 1
SP - 29
EP - 34
AB - The starting point of this note is the observation that the local condition used in the notion of a Hilbert-symbol equivalence and a quaternion-symbol equivalence — once it is expressed in terms of the Witt invariant — admits a natural generalisation. In this paper we show that for global function fields as well as the formally real function fields over a real closed field all the resulting equivalences coincide.
LA - eng
KW - Witt invariant; Brauer group; Brauer-Wall group; Witt equivalence; Witt invariant; Brauer group; Brauer-Wall group; Witt equivalence
UR - http://eudml.org/doc/35150
ER -

References

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  1. Czogała A., Równoważność Hilberta ciał globalnych, , volume 1969 of Prace Naukowe Uniwersytetu Śląskiego w Katowicach [Scientific Publications of the University of Silesia]. Wydawnictwo Uniwersytetu Śląskiego, Katowice, 2001. (1969) MR1852938
  2. Koprowski P., 10.4064/cm91-2-8, . Colloq. Math., 91(2):293–302, 2002. Zbl1030.11017MR1898636DOI10.4064/cm91-2-8
  3. Koprowski P., 10.1007/s002090100336, . Math. Z., 242(2):323–345, 2002. Zbl1067.11020MR1980626DOI10.1007/s002090100336
  4. Koprowski P., Integral equivalence of real algebraic function fields, . Tatra Mt. Math. Publ., 34:53–61, 2005. Zbl1150.11420MR2206911
  5. Lam T. Y., Introduction to quadratic forms over fields, , volume 67 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI, 2005. Zbl1068.11023MR2104929
  6. Perlis R., Szymiczek K., Conner P. E., Litherland R., 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. (1990) MR1260721
  7. Szymiczek K., Matching Witts locally and globally, . Math. Slovaca, 41(3):315–330, 1991. (1991) Zbl0766.11023MR1126669
  8. Szymiczek K., Witt equivalence of global fields, . Comm. Algebra, 19(4):1125–1149, 1991. (19(4) MR1102331
  9. Szymiczek K., Hilbert-symbol equivalence of number fields, . Tatra Mt. Math. Publ., 11:7–16, 1997. (1997) Zbl0978.11012MR1475500
  10. Szymiczek K., A characterization of tame Hilbert-symbol equivalence, . Acta Math. Inform. Univ. Ostraviensis, 6(1):191–201, 1998. (1998) Zbl1024.11022MR1822530

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