Previous |  Up |  Next


Title: Matching local Witt invariants (English)
Author: Koprowski, Przemysław
Language: English
Journal: Acta Mathematica Universitatis Ostraviensis
ISSN: 1214-8148
Volume: 13
Issue: 1
Year: 2005
Pages: 29-34
Summary lang: English
Category: math
Summary: 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. (English)
Keyword: Witt invariant
Keyword: Brauer group
Keyword: Brauer-Wall group
Keyword: Witt equivalence
MSC: 11E10
MSC: 11E81
MSC: 14H05
MSC: 14P05
MSC: 16K50
idZBL: Zbl 1251.11023
idMR: MR2290416
Date available: 2009-12-29T09:16:42Z
Last updated: 2015-03-15
Stable URL:
Reference: [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. MR 1852938
Reference: [2] Koprowski P. : Local-global principle for Witt equivalence of function fields over global fields.. Colloq. Math., 91(2):293–302, 2002. Zbl 1030.11017, MR 1898636, 10.4064/cm91-2-8
Reference: [3] Koprowski P. : Witt equivalence of algebraic function fields over real closed fields.. Math. Z., 242(2):323–345, 2002. Zbl 1067.11020, MR 1980626, 10.1007/s002090100336
Reference: [4] Koprowski P. : Integral equivalence of real algebraic function fields.. Tatra Mt. Math. Publ., 34:53–61, 2005. Zbl 1150.11420, MR 2206911
Reference: [5] Lam T. Y. : Introduction to quadratic forms over fields., volume 67 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI, 2005. Zbl 1068.11023, MR 2104929
Reference: [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. MR 1260721
Reference: [7] Szymiczek K. : Matching Witts locally and globally.. Math. Slovaca, 41(3):315–330, 1991. Zbl 0766.11023, MR 1126669
Reference: [8] Szymiczek K. : Witt equivalence of global fields.. Comm. Algebra, 19(4):1125–1149, 1991. MR 1102331
Reference: [9] Szymiczek K. : Hilbert-symbol equivalence of number fields.. Tatra Mt. Math. Publ., 11:7–16, 1997. Zbl 0978.11012, MR 1475500
Reference: [10] Szymiczek K. : A characterization of tame Hilbert-symbol equivalence.. Acta Math. Inform. Univ. Ostraviensis, 6(1):191–201, 1998. Zbl 1024.11022, MR 1822530


Files Size Format View
ActaOstrav_13-2005-1_4.pdf 242.2Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo