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Witt kernels of quadratic forms for multiquadratic extensions in characteristic 2


Author: Detlev W. Hoffmann
Journal: Proc. Amer. Math. Soc. 143 (2015), 5073-5082
MSC (2010): Primary 11E04; Secondary 11E81, 12F15
DOI: https://doi.org/10.1090/proc/12651
Published electronically: May 22, 2015
MathSciNet review: 3411127
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Abstract | References | Similar Articles | Additional Information

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$.


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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

DOI: https://doi.org/10.1090/proc/12651
Keywords: Quadratic form, bilinear form, Pfister form, Witt group, excellent extension, purely inseparable extension, exponent of an inseparable extension
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
Article copyright: © Copyright 2015 American Mathematical Society

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