| Title:
|
Graded quaternion symbol equivalence of function fields (English) |
| Author:
|
Koprowski, Przemysław |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
57 |
| Issue:
|
4 |
| Year:
|
2007 |
| Pages:
|
1311-1319 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Brauer group |
| Keyword:
|
Brauer-Wall group |
| Keyword:
|
Witt equivalence |
| MSC:
|
11E10 |
| MSC:
|
11E81 |
| MSC:
|
14H05 |
| MSC:
|
14P05 |
| MSC:
|
16K50 |
| idZBL:
|
Zbl 1190.11029 |
| idMR:
|
MR2357592 |
| . |
| Date available:
|
2009-09-24T11:53:01Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128239 |
| . |
| Reference:
|
[1] A. Czogała: Równowa.zność 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] M. Knebusch: On algebraic curves over real closed fields. II.Math. Z. 151 (1976), 189–205. Zbl 0328.14012, MR 0441979 |
| Reference:
|
[3] P. Koprowski: Local-global principle for Witt equivalence of function fields over global fields.Colloq. Math. 91 (2002), 293–302. Zbl 1030.11017, MR 1898636, 10.4064/cm91-2-8 |
| Reference:
|
[4] P. Koprowski: Witt equivalence of algebraic function fields over real closed fields.Math. Z. 242 (2002), 323–345. Zbl 1067.11020, MR 1980626, 10.1007/s002090100336 |
| Reference:
|
[5] P. Koprowski: Integral equivalence of real algebraic function fields.Tatra Mt. Math. Publ. 32 (2005), 53–61. Zbl 1150.11420, MR 2206911 |
| Reference:
|
[6] T. Y. Lam: 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:
|
[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. MR 1260721 |
| Reference:
|
[8] K. Szymiczek: Matching Witts locally and globally.Math. Slovaca 41 (1991), 315–330. Zbl 0766.11023, MR 1126669 |
| Reference:
|
[9] K. Szymiczek: Witt equivalence of global fields.Comm. Algebra 19 (1991), 1125–1149. Zbl 0724.11020, MR 1102331, 10.1080/00927879108824194 |
| Reference:
|
[10] K. Szymiczek: Hilbert-symbol equivalence of number fields.Tatra Mt. Math. Publ. 11 (1997), 7–16. Zbl 0978.11012, MR 1475500 |
| Reference:
|
[11] K. Szymiczek: A characterization of tame Hilbert-symbol equivalence.Acta Math. Inform. Univ. Ostraviensis 6 (1998), 191–201. Zbl 1024.11022, MR 1822530 |
| . |
