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Submission: 2004, Jan 30
The Hasse principle for similarity is established for restricted classes of skew-hermitian forms over quaternion division algebras with canonical involution and for hermitian forms over cyclic algebras with involution of the second kind. A counterexample is produced to show that the principle cannot hold for skew-hermitian forms over quaternion division algebras in general. This settles the two final cases of Hasse principles for similarity of forms that were missing in the literature.
2000 Mathematics Subject Classification: 16K20, 11E39, 11E12
Keywords and Phrases: Hasse principles, global fields, similarity, hermitian forms, division algebras.
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