论文标题
函子的紧凑型扩展的下降原理
A descent principle for compactly supported extensions of functors
论文作者
论文摘要
共同体具有紧凑型支持的一个特征性特性是连接空间的紧凑型共同体学组，开放子空间及其补体的长序列。鉴于代数品种的任意共同体学理论，可以询问是否存在紧凑的支持版本，以满足如此长的精确序列。每当协同理论满足抽象爆炸的下降（也称为适当的CDH下降）时，就是这种情况。我们通过证明某些类别的超轨障碍之间的等效性来确切地做到这一点。我们展示了如何从该定理中得出几种经典和非平凡的结果，例如具有紧凑型支持的独特的体重过滤。
A characteristic property of cohomology with compact support is the long exact sequence that connects the compactly supported cohomology groups of a space, an open subspace and its complement. Given an arbitrary cohomology theory of algebraic varieties, one can ask whether a compactly supported version exists, satisfying such a long exact sequence. This is the case whenever the cohomology theory satisfies descent for abstract blowups (also known as proper cdh descent). We make this precise by proving an equivalence between certain categories of hypersheaves. We show how several classical and non-trivial results, such as the existence of a unique weight filtration on cohomology with compact support, can be derived from this theorem.
