Purity for Similarity Factors

2003/09/03 by Ivan Panin, Panin, Ivan
Mathematics · #11E72 #Algebraic Geometry (math.AG) #FOS: Mathematics #K-Theory and Homology (math.KT) #math.AG #math.KT #msc:11E72

paper · pdf · doi:10.48550/arxiv.math/0309054

22 pages

arxiv created 2003/09/03 · arxiv updated 2009/12/01

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.

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