Purity for Similarity Factors
نویسنده
چکیده
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 a purity theorem for similarity factors.
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