论文标题
共同体和动机包容性排斥
Cohomological and motivic inclusion-exclusion
论文作者
论文摘要
我们将部分有序的拓扑空间和方案的包含 - 排斥原理分类为衍生的滑轮类别的过滤。结果，我们获得了函数频谱序列，这些序列概括了分层空间的两个光谱序列和某些Vassiliev型光谱序列。我们还在绿色品种环中获得了欧拉的特征类似物。作为一种应用，我们为Vakil和Wood的同源稳定性猜想提供了代数几何证明，以提供光滑的投影品种光滑的超表面段的空间。在特征零中，此猜想先前是通过拓扑方法由Aumonier建立的。
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.
