函子的紧支撑扩张的下降原理
A descent principle for compactly supported extensions of functors
AI总结：
该研究针对代数簇上同调理论的紧支撑版本是否存在满足长正合列的问题，证明了满足抽象爆破下降（真cdh下降）的上同调理论存在此类紧支撑扩张，通过超层范畴等价性精确化结论，并推导了紧支撑上同调权过滤存在性等经典结果。
摘要：
紧支撑上同调的一个特征性质是联系空间、开子空间及其补空间的紧支撑上同调群的长正合列。给定代数簇的任意上同调理论，人们可以问是否存在满足这类长正合列的紧支撑版本。只要该上同调理论满足抽象爆破下降（也称为真cdh下降），上述情况就成立。我们通过证明某些超层范畴之间的等价性来精确化这一结论。我们还展示了如何从该定理推导出若干经典且非平凡的结果，例如紧支撑上同调上唯一权过滤的存在性。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
