Quadratic and Hermitian Forms Over Rings is popular PDF and ePub book, written by Max-Albert Knus in 1991-04-05, it is a fantastic choice for those who relish reading online the Uncategoriezed genre. Let's immerse ourselves in this engaging Uncategoriezed book by exploring the summary and details provided below. Remember, Quadratic and Hermitian Forms Over Rings can be Read Online from any device for your convenience.
Quadratic and Hermitian Forms Over Rings Book PDF Summary
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.
Detail Book of Quadratic and Hermitian Forms Over Rings PDF
- Author : Max-Albert Knus
- Release : 05 April 1991
- Publisher : Unknown
- ISBN : 3642754023
- Genre : Uncategoriezed
- Total Page : 544 pages
- Language : English
- PDF File Size : 17,5 Mb
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