Ivan Panin: Purity for Similarity Factors


Submission: 2003, Sep 2

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.

2000 Mathematics Subject Classification: 11E72

Keywords and Phrases: Azumaya algebra, quadratic spaces, similarity factors, hermitian spaces

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