A Purity Theorem for Quadratic Spaces

A purity theorem for quadratic spaces over semilocal regular integral domain containing a field of odd characteristic is proved. The theorem extends results previously obtained by the author (also in collaboration with K. Pimenov) to the semilocal case. The proof is based on extending the purity theorem of Ojanguren–Panin to this more general setting. © 2022, Springer Science+Business Media, LLC, part of Springer Nature.