Annals of K-Theory

Triple linkage

Karim Johannes Becher

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Abstract

We study the condition on a field that any triple of (bilinear) Pfister forms of a given dimension are linked. This is a strengthening of the condition of linkage investigated by Elman and Lam, which asks the same for pairs of Pfister forms. In characteristic different from two this condition for triples of 2 -fold Pfister forms is related to the Hasse number.

Article information

Source
Ann. K-Theory, Volume 3, Number 3 (2018), 369-378.

Dates
Received: 14 September 2015
Revised: 12 October 2017
Accepted: 31 October 2017
First available in Project Euclid: 24 July 2018

Permanent link to this document
https://projecteuclid.org/euclid.akt/1532397762

Digital Object Identifier
doi:10.2140/akt.2018.3.369

Mathematical Reviews number (MathSciNet)
MR3830196

Zentralblatt MATH identifier
06911671

Subjects
Primary: 11E04: Quadratic forms over general fields 11E81: Algebraic theory of quadratic forms; Witt groups and rings [See also 19G12, 19G24] 19D45: Higher symbols, Milnor $K$-theory

Keywords
field Milnor $K$-theory symbol linkage bilinear Pfister form quadratic form Hasse number $u$-invariant

Citation

Becher, Karim Johannes. Triple linkage. Ann. K-Theory 3 (2018), no. 3, 369--378. doi:10.2140/akt.2018.3.369. https://projecteuclid.org/euclid.akt/1532397762


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References

  • A. Chapman, A. Dolphin, and D. B. Leep, “Triple linkage of quadratic Pfister forms”, Manuscripta Math. (online publication January 2018).
  • R. Elman, “Quadratic forms and the $u$-invariant, III”, pp. 422–444 in Conference on quadratic forms (Kingston, ON, 1976), edited by G. Orzech, Queen's Papers in Pure and Appl. Math. 46, Queen's University, Kingston, 1977.
  • R. Elman and T. Y. Lam, “Pfister forms and $K\mskip-2mu$-theory of fields”, J. Algebra 23 (1972), 181–213.
  • R. Elman and T. Y. Lam, “Quadratic forms over formally real fields and pythagorean fields”, Amer. J. Math. 94 (1972), 1155–1194.
  • R. Elman and T. Y. Lam, “Quadratic forms and the $u$-invariant, II”, Invent. Math. 21 (1973), 125–137.
  • R. Elman, T. Y. Lam, and A. Prestel, “On some Hasse principles over formally real fields”, Math. Z. 134 (1973), 291–301.
  • R. Elman, N. Karpenko, and A. Merkurjev, The algebraic and geometric theory of quadratic forms, Colloquium Publications 56, American Mathematical Society, Providence, RI, 2008.
  • T. Y. Lam, Introduction to quadratic forms over fields, Graduate Studies in Math. 67, American Mathematical Society, Providence, RI, 2005.
  • J. Milnor, “Algebraic $K\mskip-2mu$-theory and quadratic forms”, Invent. Math. 9 (1969/1970), 318–344.
  • E. Peyre, “Products of Severi–Brauer varieties and Galois cohomology”, pp. 369–401 in $K\mskip-2mu$-theory and algebraic geometry: connections with quadratic forms and division algebras (Santa Barbara, CA, 1992), vol. 2, edited by W. B. Jacob and A. Rosenberg, Proceedings of Symposia in Pure Math. 58, American Mathematical Society, Providence, RI, 1995.
  • A. Pfister, Quadratic forms with applications to algebraic geometry and topology, London Mathematical Society Lecture Note Series 217, Cambridge University Press, 1995.
  • A. Prestel and R. Ware, “Almost isotropic quadratic forms”, J. London Math. Soc. $(2)$ 19:2 (1979), 241–244.
  • A. S. Sivatski, “Linked triples of quaternion algebras”, Pacific J. Math. 268:2 (2014), 465–476.