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- W2018939903 abstract "Let A be a regular local ring and K its field of fractions. We denote by W the Witt group functor that classifies quadratic spaces. We say that purity holds for A if W(A) is the intersection of all W(Ap) ⊂ W(K), as p runs over the height-one prime ideals of A. We prove purity for every regular local ring containing a field of characteristic ≠ 2. The question of purity and of the injectivity of W(A) into W(K) for arbitrary regular local rings is still open. Soit A un anneau local régulier et K son corps des fractions. Soit W le foncteur groupe de Witt qui classifie les espaces quadratiques. On dit que le théorème de pureté vaut pour A si W(A) est l'intersection de tous les W(Ap) ⊂ W(K), oùp parcourt les idéaux premiers de hauteur égale à 1 de A. Nous démontrons le théorème de pureté pour tout anneau local régulier qui contient un corps de caractéristique ≠ 2. La question de la pureté et de l'injectivité de W(A) dans W(K) pour un anneau local régulier arbitraire est encore ouverte." @default.
- W2018939903 created "2016-06-24" @default.
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- W2018939903 date "1999-01-01" @default.
- W2018939903 modified "2023-10-16" @default.
- W2018939903 title "A purity theorem for the witt group" @default.
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- W2018939903 doi "https://doi.org/10.1016/s0012-9593(99)80009-3" @default.
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