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SPRINGER'S ODD DEGREE EXTENSION THEOREM FOR QUADRATIC FORMS OVER SEMILOCAL RINGS

Abstract : A fundamental result of Springer says that a quadratic form over a field of characteristic not 2 is isotropic if it is so after an odd degree extension. In this paper we generalize Springer's theorem as follows. Let R be a an arbitrary semilocal ring, let S be a finite R-algebra of odd degree, which is étale or generated by one element, and let q be a nonsingular R-quadratic form whose base ring extension q S is isotropic. We show that then q is already isotropic.
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Preprints, Working Papers, ...
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https://hal-cnrs.archives-ouvertes.fr/hal-03124810
Contributor : Philippe Gille <>
Submitted on : Friday, January 29, 2021 - 12:15:28 PM
Last modification on : Thursday, February 4, 2021 - 10:27:41 AM

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  • HAL Id : hal-03124810, version 1
  • ARXIV : 2101.12553

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Philippe Gille, Erhard Neher. SPRINGER'S ODD DEGREE EXTENSION THEOREM FOR QUADRATIC FORMS OVER SEMILOCAL RINGS. 2021. ⟨hal-03124810⟩

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