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Line-bundle-valued ternary quadratic forms over schemes
Published in Elsevier BV
2007
Volume: 208
   
Issue: 1
Pages: 237 - 259
Abstract

We study degenerations of rank 3 quadratic forms and of rank 4 Azumaya algebras, and extend what is known for good forms and Azumaya algebras. By considering line-bundle-valued forms, we extend the theorem of Max-Albert Knus that the Wittinvariant—the even Clifford algebra of a form—suffices for classification. An algebra Zariski-locally the even Clifford algebra of a ternary form is so globally up to twisting by square roots of line bundles. The general, usual and special orthogonal groups of a form are determined in terms of automorphism groups of its Witt-invariant. Martin Kneser’s characteristic-free notion of semiregular form is used.

About the journal
JournalData powered by TypesetJournal of Pure and Applied Algebra
PublisherData powered by TypesetElsevier BV
Open AccessNo