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Powers of the Fundamental Ideal in the Witt Ring

✍ Scribed by Jón Kr. Arason; Richard Elman

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
100 KB
Volume
239
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

✦ Synopsis

Let K be a field of characteristic different from 2. In the algebraic theory of Ž . quadratic forms, one studies the Witt ring W K of equivalence classes of non-den Ž . generate quadratic forms. The Witt ring has a filtration given by the powers I K Ž . n Ž . of the fundamental ideal I K of even-dimensional forms. The ideal I K is Ž . ²² :: generated by the set P K of n-fold Pfister forms, a , . . . , a [

m 1, ya , where a g K s K _ 0 . Many questions about this filtration and i i is1

Ž . its quotients have arisen in the study of W K . The spectacular work of Voevodsky, together with his collaborative work with Orlov and Vishik, allows one to answer many old questions. The purpose of this paper is to indicate some of these solutions.

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