Quelques remarques sur le u -invariant

B. Kahn

Journal de théorie des nombres de Bordeaux (1990)

  • Volume: 2, Issue: 1, page 155-161
  • ISSN: 1246-7405

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Kahn, B.. "Quelques remarques sur le $u$-invariant." Journal de théorie des nombres de Bordeaux 2.1 (1990): 155-161. <http://eudml.org/doc/93509>.

@article{Kahn1990,
author = {Kahn, B.},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {products of quaternion algebras; u-invariant; anisotropic quadratic forms; cohomological dimension; Brauer group; Witt ring},
language = {fre},
number = {1},
pages = {155-161},
publisher = {Université Bordeaux I},
title = {Quelques remarques sur le $u$-invariant},
url = {http://eudml.org/doc/93509},
volume = {2},
year = {1990},
}

TY - JOUR
AU - Kahn, B.
TI - Quelques remarques sur le $u$-invariant
JO - Journal de théorie des nombres de Bordeaux
PY - 1990
PB - Université Bordeaux I
VL - 2
IS - 1
SP - 155
EP - 161
LA - fre
KW - products of quaternion algebras; u-invariant; anisotropic quadratic forms; cohomological dimension; Brauer group; Witt ring
UR - http://eudml.org/doc/93509
ER -

References

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  1. [ART] S.A. Amitsur, L-H. Rowen, J-P. Tignol, Division algebras of degree 4 and 8 with involutionIsrael J. Math.33 (1979), 133-148. Zbl0422.16010MR571249
  2. [CG] J-P. Serre, Cohomologie galoisienne, Lect. Notes in Math. 5. Springer, Berlin, 1965. Zbl0136.02801MR201444
  3. [EL] R. Elman, T.Y. Lam, On the quaternion symbol homomorphism 9F: k2F → B(F), Lect. Notes in Math. 342, 447-463. Springer, New-York, 1973. Zbl0267.10030
  4. [ELTW] R. Elman, T.Y. Lam, J-P. Tignol, A. Wadsworth, Witt rings and Brauer groups under multiquadratic extensions, I, Amer. J. Math105 (1983), 1119-1170. Zbl0492.10014MR714772
  5. [G] M. Greenberg, Lectures on forms in many variables. Benjamin, New York, 1969. Zbl0185.08304MR241358
  6. [K] I. KaplanskyQuadratic forms, J. Soc. Math. Japan5 (1953), 200-207. Zbl0051.02902MR59260
  7. [Lam] T.Y. Lam, The algebraic theory of quadratic forms. Benjamin, New-York, 1980. Zbl0437.10006MR396410
  8. [M] A.S. Merkurjev, Simple algebras over function fields of quadrics. preprint, 1989. 
  9. [MS] A.S. Merkurjev, A.A. Suslin, K-cohomology of Severi-Brauer varieties and the norm residue homomorphism, Izv. Akad. Nauk SSSR46 (1982), 1011-1046. Trad. anglaise: Math. USSR Izv.21 (1983), 307-341. Zbl0525.18008MR675529
  10. [R] M.L. Racine, A simple proof of theorem of Albert, Proc. AMS43 (1974), 487-488. Zbl0285.16013MR330218
  11. [T1] J-P. Tignol, Sur les classes de similitude de corps à involution de degré 8, C.R. Acad. Sci. Paris286. Zbl0374.16006MR498496
  12. [T2] J-P. Tignol, Réduction de l'indice d'une algébre simple sur le corps des fonctions d'une quadrique. preprint, 1989. 
  13. [T3] J-P. Tignol, On the length of decompositions of central simple algebras in tensor products of symbols, in Methods of ring theory, NATO ASI Series, Ser. C129, 505-516. Reidel, Dordrecht, 1984. Zbl0558.16010MR770614

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