Cohomological and motivic inclusion–exclusion

IF 1.3 1区 数学 Q1 MATHEMATICS Compositio Mathematica Pub Date : 2024-09-13 DOI:10.1112/s0010437x24007292
Ronno Das, Sean Howe
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引用次数: 0

Abstract

We categorify the inclusion–exclusion principle for partially ordered topological spaces and schemes to a filtration on the derived category of sheaves. As a consequence, we obtain functorial spectral sequences that generalize the two spectral sequences of a stratified space and certain Vassiliev-type spectral sequences; we also obtain Euler characteristic analogs in the Grothendieck ring of varieties. As an application, we give an algebro-geometric proof of Vakil and Wood's homological stability conjecture for the space of smooth hypersurface sections of a smooth projective variety. In characteristic zero this conjecture was previously established by Aumonier via topological methods.

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同构和动机包含-排除
我们将部分有序拓扑空间和方案的包含-排除原理归类为剪子派生类的滤波。因此,我们得到了泛化了分层空间的两个谱序列和某些瓦西里耶夫型谱序列的扇形谱序列;我们还得到了格罗内狄克环中的欧拉特征类似物。作为应用,我们给出了瓦基尔和伍德关于光滑投影变种的光滑超曲面部分空间的同调稳定性猜想的几何证明。在零特征中,奥莫尼埃曾通过拓扑方法建立了这一猜想。
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来源期刊
Compositio Mathematica
Compositio Mathematica 数学-数学
CiteScore
2.10
自引率
0.00%
发文量
62
审稿时长
6-12 weeks
期刊介绍: Compositio Mathematica is a prestigious, well-established journal publishing first-class research papers that traditionally focus on the mainstream of pure mathematics. Compositio Mathematica has a broad scope which includes the fields of algebra, number theory, topology, algebraic and differential geometry and global analysis. Papers on other topics are welcome if they are of broad interest. All contributions are required to meet high standards of quality and originality. The Journal has an international editorial board reflected in the journal content.
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