# Josefien Kuijper: A general blowup-principle for compact support extensions of functors

**Time: **
Tue 2021-12-07 11.00 - 12.00

**Location: **
Institut Mittag-Leffler, Seminar Hall Kuskvillan (alt. Zoom, 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 triangulated category *T*, one can wonder when it makes sense to define 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 *T*-valued sheaves on different sites of varieties. I will discuss several applications of this theorem.