Graded quaternion symbol equivalence of function fields

Przemysław Koprowski

Czechoslovak Mathematical Journal (2007)

  • Volume: 57, Issue: 4, page 1311-1319
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Koprowski, Przemysław. "Graded quaternion symbol equivalence of function fields." Czechoslovak Mathematical Journal 57.4 (2007): 1311-1319. <http://eudml.org/doc/31194>.

@article{Koprowski2007,
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.},
author = {Koprowski, Przemysław},
journal = {Czechoslovak Mathematical Journal},
keywords = {Brauer group; Brauer-Wall group; Witt equivalence; quaternion-symbol equivalence; Brauer group},
language = {eng},
number = {4},
pages = {1311-1319},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Graded quaternion symbol equivalence of function fields},
url = {http://eudml.org/doc/31194},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Koprowski, Przemysław
TI - Graded quaternion symbol equivalence of function fields
JO - Czechoslovak Mathematical Journal
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 57
IS - 4
SP - 1311
EP - 1319
AB - 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.
LA - eng
KW - Brauer group; Brauer-Wall group; Witt equivalence; quaternion-symbol equivalence; Brauer group
UR - http://eudml.org/doc/31194
ER -

References

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  7. 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. MR1260721
  8. Matching Witts locally and globally, Math. Slovaca 41 (1991), 315–330. (1991) Zbl0766.11023MR1126669
  9. 10.1080/00927879108824194, Comm. Algebra 19 (1991), 1125–1149. (1991) Zbl0724.11020MR1102331DOI10.1080/00927879108824194
  10. Hilbert-symbol equivalence of number fields, Tatra Mt. Math. Publ. 11 (1997), 7–16. (1997) Zbl0978.11012MR1475500
  11. A characterization of tame Hilbert-symbol equivalence, Acta Math. Inform. Univ. Ostraviensis 6 (1998), 191–201. (1998) Zbl1024.11022MR1822530

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