Witt kernels of bilinear forms for algebraic extensions in characteristic

Author:
Detlev W. Hoffmann

Journal:
Proc. Amer. Math. Soc. **134** (2006), 645-652

MSC (2000):
Primary 11E04; Secondary 11E81, 12F15

Published electronically:
August 29, 2005

MathSciNet review:
2180880

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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.

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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:
http://dx.doi.org/10.1090/S0002-9939-05-08175-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

Published electronically:
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

Article copyright:
© Copyright 2005
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.