Download this article
 Download this article For screen
For printing
Recent Issues
Volume 8, Issue 4
Volume 8, Issue 3
Volume 8, Issue 2
Volume 8, Issue 1
Volume 7, Issue 4
Volume 7, Issue 3
Volume 7, Issue 2
Volume 7, Issue 1
Volume 6, Issue 4
Volume 6, Issue 3
Volume 6, Issue 2
Volume 6, Issue 1
Volume 5, Issue 4
Volume 5, Issue 3
Volume 5, Issue 2
Volume 5, Issue 1
Volume 4, Issue 4
Volume 4, Issue 3
Volume 4, Issue 2
Volume 4, Issue 1
Volume 3, Issue 4
Volume 3, Issue 3
Volume 3, Issue 2
Volume 3, Issue 1
Volume 2, Issue 4
Volume 2, Issue 3
Volume 2, Issue 2
Volume 2, Issue 1
Volume 1, Issue 4
Volume 1, Issue 3
Volume 1, Issue 2
Volume 1, Issue 1
The Journal
About the Journal
Editorial Board
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 2379-1691 (e-only)
ISSN: 2379-1683 (print)
Author Index
To Appear
 
Other MSP Journals
A descent principle for compactly supported extensions of functors

Josefien Kuijper

Vol. 8 (2023), No. 3, 489–529
Abstract

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 nontrivial results, such as the existence of a unique weight filtration on cohomology with compact support, can be derived from this theorem.

Keywords
proper cdh descent, cohomology with compact support, varieties
Mathematical Subject Classification
Primary: 14F99
Secondary: 14F42, 18F10, 55U99
Milestones
Received: 12 December 2022
Revised: 11 May 2023
Accepted: 2 June 2023
Published: 27 August 2023
Authors
Josefien Kuijper
Department of Mathematics
Stockholm University
Stockholm
Sweden