|
Witt kernels of bilinear forms for algebraic extensions in characteristic 
Author(s):
Detlev
W.
Hoffmann
Journal:
Proc. Amer. Math. Soc.
134
(2006),
645-652.
MSC (2000):
Primary 11E04;
Secondary 11E81, 12F15
Posted:
August 29, 2005
Retrieve article in:
PDF DVI PostScript
Abstract |
References |
Similar articles |
Additional information
Abstract:
Let  be a field of characteristic  and let  be a purely inseparable extension of exponent  . We determine the kernel  of the natural restriction map  between the Witt rings of bilinear forms of  and  , respectively. This complements a result by Laghribi who computed the kernel for the Witt groups of quadratic forms for such an extension  . Based on this result, we will determine  for a wide class of finite extensions which are not necessarily purely inseparable.
References:
-
- 1.
- R. Baeza, Ein Teilformensatz für quadratische Formen in Charakteristik
 , Math. Z. 135 (1974), 175-184. MR 0337765 (49:2534) - 2.
- R. Baeza, Quadratic forms over semi-local rings, Lecture Notes in Mathematics, vol. 655, Springer-Verlag, 1976. MR 0491773 (58:10972)
- 3.
- R. Elman, T.Y. Lam, and A. Wadsworth, Amenable fields and Pfister extensions, Proc. of Quadratic Forms Conference, Queen's Univ., Kingston, Ont., 1976 (G. Orzech, ed.). Queen's Papers in Pure and Applied Mathematics No. 46 (1977), 445-491. MR 0560497 (58:27756)
- 4.
- D. Hoffmann, Diagonal forms of degree
 in characteristic  , Algebraic and Arithmetic Theory of Quadratic Forms, 135-183, Contemp. Math., 344, Amer. Math. Soc., Providence, RI, 2004. MR 2058673 - 5.
- I. Kaplansky, Fields and Rings, 2nd ed., Chicago Lectures in Mathematics, The University of Chicago Press, Chicago, Ill.-London, 1972. MR 0349646 (50:2139)
- 6.
- K. Kato, Symmetric bilinear forms, quadratic forms and Milnor
 -theory in characteristic two, Invent. Math. 66 (1982), 493-510. MR 0662605 (83i:10027) - 7.
- A. Laghribi, Witt kernels of quadratic forms for multiquadratic extensions in characteristic
 , preprint 2004. - 8.
- A. Pfister, Quadratic Forms with Applications to Algebraic Geometry and Topology, London Math. Soc. Lecture Note Series, vol. 217, Cambridge University Press, Cambridge, 1995. MR 1366652 (97c:11046)
- 9.
- M. Weisfeld, Purely inseparable extensions and higher derivations, Trans. Amer. Math. Soc. 116 (1965), 435-449. MR 0191895 (33:122)
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(2000):
11E04,
11E81, 12F15
Retrieve articles in all Journals with MSC
(2000):
11E04,
11E81, 12F15
Additional Information:
Detlev
W.
Hoffmann
Affiliation:
School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
Email:
detlev.hoffmann@nottingham.ac.uk
DOI:
10.1090/S0002-9939-05-08175-X
PII:
S 0002-9939(05)08175-X
Keywords:
Quadratic form,
bilinear form,
Pfister form,
Witt ring,
excellent extension,
purely inseparable extension,
exponent of an inseparable extension,
balanced extension
Received by editor(s):
October 10, 2004
Posted:
August 29, 2005
Additional Notes:
The research on this paper was supported in part by the European research network HPRN-CT-2002-00287 ``Algebraic $K$-Theory, Linear Algebraic Groups and Related Structures''.
Dedicated:
In memory of Professor Martin Kneser
Communicated by:
Bernd Ulrich
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|
Comments: webmaster@ams.org