Quadratic and Hermitian Forms Over Rings

Released on by Max-Albert Knus
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  • Quadratic and Hermitian Forms Over Rings Book Detail

  • Author : Max-Albert Knus
  • Release Date : 1991-04-05
  • Publisher :
  • Genre :
  • Pages : 544
  • ISBN 13 : 9783642754029
  • File Size : 84,84 MB
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Quadratic and Hermitian Forms Over Rings by Max-Albert Knus PDF Summary

Book Description: This book presents the theory of quadratic and hermitian forms over rings in a very general setting. It avoids, as far as possible, any restriction on the characteristic and takes full advantage of the functorial properties of the theory. It is not an encyclopedic survey. It stresses the algebraic aspects of the theory and avoids - within reason - overlapping with other books on quadratic forms (like those of Lam, Milnor-Husemoller and Scharlau). One important tool is descent theory with the corresponding cohomological machinery. It is used to define the classical invariants of quadratic forms, but also for the study of Azmaya algebras, which are fundamental in the theory of Clifford algebras. Clifford algebras are applied, in particular, to treat in detail quadratic forms of low rank and their spinor groups. Another important tool is algebraic K-theory, which plays the role that linear algebra plays in the case of forms over fields. The book contains complete proofs of the stability, cancellation and splitting theorems in the linear and in the unitary case. These results are applied to polynomial rings to give quadratic analogues of the theorem of Quillen and Suslin on projective modules. Another, more geometric, application is to Witt groups of regular rings and Witt groups of real curves and surfaces.

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Quadratic and Hermitian Forms Over Rings

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Quadratic and Hermitian Forms over Rings

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From its birth (in Babylon?) till 1936 the theory of quadratic forms dealt almost exclusively with forms over the real field, the complex field or the ring of i