On the convergence of the orthogonal spectral sequence

IF 0.8 4区数学 Q2 MATHEMATICS

Homology Homotopy and Applications Pub Date : 2021-11-05 DOI:10.4310/hha.2022.v24.n2.a20

César Galindo, Pablo Peláez

引用次数: 0

Abstract

We show that the orthogonal spectral sequence introduced by the second author is strongly convergent in Voevodsky's triangulated category of motives DM over a field k. In the context of the Morel-Voevodsky motivic stable homotopy category we provide concrete examples where the spectral sequence is not strongly convergent, and give a criterion under which the strong convergence still holds. This criterion holds for Voevodsky's slices, and as a consequence we obtain a spectral sequence which converges strongly to the E1-term of Voevodsky's slice spectral sequence.

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正交谱序列的收敛性

我们证明了由第二作者引入的正交谱序列在Voevodsky的动机的三角范畴DM中在域k上是强收敛的。在Morel-Voevodsky动机稳定同伦范畴中，我们给出了谱序列不强收敛的具体例子，并给出了谱序列仍然强收敛的判据。该准则适用于Voevodsky的切片，因此我们得到了一个强收敛于Voevodsky的切片谱序列的e1项的谱序列。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Homology Homotopy and Applications 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Homology, Homotopy and Applications is a refereed journal which publishes high-quality papers in the general area of homotopy theory and algebraic topology, as well as applications of the ideas and results in this area. This means applications in the broadest possible sense, i.e. applications to other parts of mathematics such as number theory and algebraic geometry, as well as to areas outside of mathematics, such as computer science, physics, and statistics. Homotopy theory is also intended to be interpreted broadly, including algebraic K-theory, model categories, homotopy theory of varieties, etc. We particularly encourage innovative papers which point the way toward new applications of the subject.