| 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:
|
http://hdl.handle.net/10338.dmlcz/137469 |
| . |
| 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 |
| . |
