Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
|
   
Mobile Device Pairing
 Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

Witt kernels of quadratic forms for purely inseparable multiquadratic extensions in characteristic 2


Author: Ahmed Laghribi
Journal: Proc. Amer. Math. Soc. 134 (2006), 2481-2486
MSC (2000): Primary 11E04, 11E81
Posted: April 13, 2006
MathSciNet review: 2213724
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The aim of this paper is to give a complete answer to the question of hyperbolicity of nonsingular quadratic forms over purely inseparable multiquadratic extensions in characteristic $ 2$. This completes partial computations of Mammone and Moresi.

References

  • [A] H. Ahmad,
    Witt kernels of bi-quadratic extensions in characteristic $ 2$,
    Bull. Austral. Math. Soc. 69 (2004), 433-440. MR 2066661 (2005g:11058a)
  • [AB] R. Aravire, R. Baeza,
    The behavior of quadratic and differential forms under function field extensions in characteristic two,
    J. Algebra 259 (2003), 361-414. MR 1955526 (2003k:11060)
  • [B1] R. Baeza,
    Ein Teilformensatz für quadratische Formen in Charakteristik $ 2$,
    Math. Z. 135 (1974), 175-184. MR 0337765 (49:2534)
  • [B2] R. Baeza,
    Quadratic forms over semilocal rings,
    Lect. Notes Math. vol. 655, Berlin, Heidelberg, New York, Springer 1978. MR 0491773 (58:10972)
  • [ELTW] R. Elman, T. Y. Lam, J.-P. Tignol, A. Wadsworth,
    Witt rings and Brauer groups under multiquadratic extensions I,
    Amer. J. Math. 105 (1983), 1119-1170. MR 0714772 (85i:11032)
  • [ELW] R. Elman, T. Y. Lam, A. Wadsworth,
    Quadratic forms under multiquadratic extensions,
    Indag. Math. 42 (1980), 131-145. MR 0577569 (81j:10028)
  • [HL] D. W. Hoffmann, A. Laghribi,
    Quadratic forms and Pfister neighbors in characteristic $ 2$, Trans. Amer. Math. Soc. 356 (2004), 4019-4053. MR 2058517 (2005e:11041)
  • [K] K. Kato,
    Symmetric bilinear forms, quadratic forms and Milnor K-theory in characteristic $ 2$,
    Inventiones Math. 66 (1982), 493-510. MR 0662605 (83i:10027)
  • [L1] A. Laghribi,
    Certaines formes quadratiques de dimension au plus $ 6$ et corps des fonctions en caractéristique $ 2$,
    Israel J. Math. 129 (2002), 317-361. MR 1910948 (2003f:11047)
  • [L2] A. Laghribi,
    Witt kernels of function field extensions in characteristic $ 2$, J. Pure Appl. Algebra 199 (2005), 167-182. MR 2134299 (2006c:11041)
  • [MM] P. Mammone, R. Moresi,
    Formes quadratiques, algèbres à division et extensions multiquadratiques inséparables,
    Bull. Belg. Math. Soc. 2 (1995), 311-319. MR 1338463 (96j:11052)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 11E04, 11E81

Retrieve articles in all journals with MSC (2000): 11E04, 11E81

Additional Information

Ahmed Laghribi
Affiliation: Laboratoire de Mathématiques de Lens EA 2462, Faculté des Sciences Jean Perrin, rue Jean Souvraz - SP18, F-62307 Lens, France
Email: laghribi@euler.univ-artois.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08649-7
PII: S 0002-9939(06)08649-7
Keywords: Nonsingular quadratic forms, Witt groups, Witt kernels, differential forms.
Received by editor(s): July 26, 2004
Received by editor(s) in revised form: January 7, 2005
Posted: April 13, 2006
Additional Notes: The author was supported by the European research network HPRN-CT-2002-00287 ``Algebraic $K$-Theory, Linear Algebraic Groups and Related Structures''.
Communicated by: Lance W. Small
Article copyright: © Copyright 2006 American Mathematical Society




AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia