A descent principle for compact support extensions of functors
Abstract
A characteristic property of compact support cohomology is the long exact sequence that connects the compact support cohomology groups of a space, an open subspace and its complement. Given an arbitrary cohomology theory of algebraic varieties, one can ask whether a compact support 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 nontrivial results, such as the existence of a unique weight filtration on compact support cohomology, can be derived from this theorem.
 Publication:

arXiv eprints
 Pub Date:
 April 2022
 DOI:
 10.48550/arXiv.2204.08968
 arXiv:
 arXiv:2204.08968
 Bibcode:
 2022arXiv220408968K
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Algebraic Topology;
 Mathematics  KTheory and Homology;
 14F99 (primary);
 18F10;
 55U99;
 14F42 (secondary)
 EPrint:
 32 pages. Minor revisions for clarity, simpler proof of Proposition 5.2. Comments are welcome!