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

**Time: **
Wed 2021-12-08 10.15 - 11.15

**Location: **
Kräftriket, House 6, Room 306 (also on Zoom)

**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 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 *C*-valued sheaves on different sites of varieties. I will discuss several applications of this theorem.