Purity for Similarity Factors
Algebraic Geometry
2007-05-23 v1 K-Theory and Homology
Abstract
Two Azumaya algebras with involutions are considered over a regular local ring. It is proved that if they are isomorphic over the quotient field, then they are isomorphic too. In particular, if two quadratic spaces over such a ring are similar over its quotient field, then these two spaces are similar already over the ring. The result is a consequence of a purity theorem for similarity factors proved in this text and the known fact that rationally isomorphic hermitian spases are locally isomorphic.
Cite
@article{arxiv.math/0309054,
title = {Purity for Similarity Factors},
author = {Ivan Panin},
journal= {arXiv preprint arXiv:math/0309054},
year = {2007}
}
Comments
22 pages