Witt kernels of quadratic forms for multiquadratic extensions in characteristic 2
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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 show that the extension is excellent for quadratic forms. Using the excellence, we recover and extend results by Aravire and Laghribi who computed generators for the kernel $W_q(K/F)$ of the natural restriction map $W_q(F)\to W_q(K)$ between the Witt groups of quadratic forms of $F$ and $K$, respectively, where $K/F$ is a finite multiquadratic extension of separability degree at most $2$.References
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Additional Information
- Detlev W. Hoffmann
- Affiliation: Fakultät für Mathematik, Technische Universität Dortmund, 44221 Dortmund, Germany
- Email: detlev.hoffmann@math.tu-dortmund.de
- Received by editor(s): March 7, 2014
- Received by editor(s) in revised form: September 16, 2014
- Published electronically: May 22, 2015
- Additional Notes: The research on this paper was supported in part by the DFG Projekt “Annihilators and kernels in Kato’s cohomology in positive characteristic and in Witt groups in characteristic $2$”.
- Communicated by: Matthew A. Papanikolas
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 143 (2015), 5073-5082
- MSC (2010): Primary 11E04; Secondary 11E81, 12F15
- DOI: https://doi.org/10.1090/proc/12651
- MathSciNet review: 3411127