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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Witt kernels of bilinear forms for algebraic extensions in characteristic $2$


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: Let $F$ be a field of characteristic $2$ and let $K/F$ be a purely inseparable extension of exponent $1$. We determine the kernel $W(K/F)$ of the natural restriction map $WF\to WK$between the Witt rings of bilinear forms of $F$ and $K$, respectively. This complements a result by Laghribi who computed the kernel for the Witt groups of quadratic forms for such an extension $K/F$. Based on this result, we will determine $W(K/F)$ 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
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
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.