论文标题
动机环境中的本地化频谱序列
The localization spectral sequence in the motivic setting
论文作者
论文摘要
我们构建和研究了与分层方案相关的光谱序列的动机提升，彼得森最近在混合霍奇理论和$ \ ell $ - ad-adic galois表示的背景下发现。原始频谱序列根据地层封闭的紧凑型共同体和分层基础的POSET的组合表达了开放层的紧凑型共同体。它的一些特殊情况是研究次视和配置空间的经典工具。我们的动机提升生活在三角构象类的类别中，并采用了尼科夫后系统的形状。我们描述了它的连接形态，并研究了其一些功能性能。
We construct and study a motivic lift of a spectral sequence associated to a stratified scheme, recently discovered by Petersen in the context of mixed Hodge theory and $\ell$-adic Galois representations. The original spectral sequence expresses the compactly supported cohomology of an open stratum in terms of the compactly supported cohomology of the closures of strata and the combinatorics of the poset underlying the stratification. Some of its special cases are classical tools in the study of arrangements of subvarieties and configuration spaces. Our motivic lift lives in the triangulated category of étale motives and takes the shape of a Postnikov system. We describe its connecting morphisms and study some of its functoriality properties.
