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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- Detlev W. Hoffmann
- Affiliation: School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
- Email: email@example.com
- 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”.
- Communicated by: Bernd Ulrich
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
- Journal: Proc. Amer. Math. Soc. 134 (2006), 645-652
- MSC (2000): Primary 11E04; Secondary 11E81, 12F15
- DOI: https://doi.org/10.1090/S0002-9939-05-08175-X
- MathSciNet review: 2180880
Dedicated: In memory of Professor Martin Kneser