Abstract
Let R be a regular local ring, K its field of fractions and A1, A2 two Azumaya algebras with involutions over R. We show that if A1 ⊗ R K and A1 ⊗ R K are isomorphic over K, then A1 and A2 are isomorphic over R. In particular, if two quadratic spaces over the ring R become similar over K then these two spaces are similar already over R. The results are consequences of three facts:(a) rationally isomorphic hermitian spaces are locally isomorphic, (b) the results hold for discrete valuation ring, (c) a purity theorem hold for multipliers.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
