On the Witt group of the punctured spectrum of a regular semilocal ring

IF 1 2区数学 Q1 MATHEMATICS

Journal of the London Mathematical Society-Second Series Pub Date : 2024-12-05 DOI:10.1112/jlms.70042

Stefan Gille, Ivan Panin

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引用次数: 0

Abstract

Let $R$ be a regular semilocal ring of dimension $4 q + 1 ⩾ 5$ which contains $\frac{1}{2}$ , $l ⩾ 1$ the number of maximal ideals of $R$ which are assumed to be all of the same height, and $U$ the punctured spectrum of $R$ , that is, $Spec R$ without the maximal ideals. We show that the Witt ring $W (U)$ of $U$ has $l$ non-trivial generators $E_{1}, …, E_{l}$ as $W (R)$ -algebra, which satisfy $E_{i} E_{j} = 0$ for all $1 ⩽ i, j ⩽ l$ . If $R$ is integral, then these generators become trivial over the fraction field $K$ of $R$ . In particular, the natural morphism $W (U) ⟶ W (K)$ is not injective.

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来源期刊

Journal of the London Mathematical Society-Second Series 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

186

审稿时长

6-12 weeks

期刊介绍： The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.