# Josefien Kuijper: Postdoc day, Seminar 1: A general descent principle for compact support extensions

**Time: **
Fri 2022-04-01 14.15 - 14.45

**Location: **
Institut Mittag-Leffler, Seminar Hall Kuskvillan and Zoom

**Video link: **
Meeting ID: 921 756 1880

**Participating: **
Josefien Kuijper (Stockholm University)

**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 invariant of algebraic varieties, taking values in a stable infinity-category *C*, one can wonder under what conditions it is possible to construct a “compact support” version of the invariant in such a way that this long exact sequence exists by construction. In this talk I give an answer to this question, in the form of an equivalence of categories of *C*-valued hypersheaves on different sites of algebraic varieties. I will discuss some applications of this theorem.