The standard filtration on cohomology with compact supports with an appendix on the base change map and the Lefschetz hyperplane theorem
The standard filtration on cohomology with compact supports with an appendix on the base change map and the Lefschetz hyperplane theorem
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带有紧支撑的上同调的标准过滤，带有基变图上的附录和 Lefschetz 超平面定理
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发表时间：
2009
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通讯作者：
M. A. Cataldo
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作者：
M. A. Cataldo
在可构造复合体上，利用相关簇的部分紧化上的超平面截面标记，描述了具有紧支撑的拟射影簇的上同群上的标准滤波和Leray滤波。证明的关键成分之一是反常束的Lefschetz超平面定理，在附录中，我们讨论了代数变异上可构造束的基变化映射及其在Lefschetz超平面定理证明中的作用，由Beilinson给出。
We describe the standard and Leray filtrations on the cohomology groups with compact supports of a quasi projective variety with coefficients in a constructible complex using flags of hyperplane sections on a partial compactification of a related variety. One of the key ingredients of the proof is the Lefschetz hyperplane theorem for perverse sheaves and, in an appendix, we discuss the base change maps for constructible sheaves on algebraic varieties and their role in a proof, due to Beilinson, of the Lefschetz hyperplane theorem.