Quadratic Spaces and Orthogonal Groups over semilocal Rings

Philippe Gille; Erhard Neher

Quadratic Spaces and Orthogonal Groups over semilocal Rings

Algebraic Geometry 2026-06-29 v1 Rings and Algebras

Authors: Philippe Gille , Erhard Neher

Abstract

We prove Springer's Odd Degree Theorem for quadratic forms over LG rings, and Scharlau's and Knebusch's norm principles for quadratic forms over semilocal rings. We present applications to the flat cohomology of spin groups and {\'e}tale norm groups.

Keywords

quadratic forms semilocal rings Springer's theorem norm principles spin groups flat cohomology

Cite

@article{arxiv.2606.30057,
  title  = {Quadratic Spaces and Orthogonal Groups over semilocal Rings},
  author = {Philippe Gille and Erhard Neher},
  journal= {arXiv preprint arXiv:2606.30057},
  year   = {2026}
}