Springer's odd degree extension theorem for quadratic forms over semilocal rings
Rings and Algebras
2021-06-22 v2
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 constant odd degree, which is {\'e}tale 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.
Cite
@article{arxiv.2101.12553,
title = {Springer's odd degree extension theorem for quadratic forms over semilocal rings},
author = {Philippe Gille and Erhard Neher},
journal= {arXiv preprint arXiv:2101.12553},
year = {2021}
}