Quadratic and Hermitian Forms over Rings

Presenting the theory of quadratic and hermitian forms over rings in an algebraic setting, this textbook features a detailed study of Clifford algebras and complete proofs of the stability, cancellation and splitting theorems in unitary K-theory.

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This book presents the theory of quadratic and hermitian forms over rings in a very general setting. It avoids any restriction on characteristics and takes full advantage of the functorial properties of the theory. Emphasis is placed on algebraic aspects of the theory. The text also defines descent theory, with its corresponding cohomological machinery. Clifford algebras are additionally applied, specifically to treat in detail the quadratic forms of low rank and their spinor groups. The text also covers the stability, cancellation and splitting theorems in unitary K-theory. These theorems are applied to polynomial rings, to give quadratic analogues of the theorem of Quillen and Suslin on projective modules, and to Witt groups of regular rings.