# Thomas Kragh: Non-connective K-theory

Time: Fri 2020-06-26 10.15 - 12.00

Lecturer: Thomas Kragh

Location:

This is the last talk of the seminar on algebraic K-theory and derived algebraic geometry

The seminar will be held via Zoom.

Abstract:

In this talk I will motivate and define non-connective K
theory (for \infty-categories). As an example I will discus
non-connective K theory of quasi-compact and quasi-separable schemes and
Weibel's conjecture. I will also discus the fact that non-connective K
theory is a so-called localizing invariant and in fact the initial such
(if consider together with its natural transformation in a certain
category of natural transformations). The localizing invariant condition
is a slightly more restrictive version of being an additive invariant
for which the standard K theory (with its natural transformation) is
initial (as we saw in Kristian's talk). If time permits I will discus
why topological Hochschild homology (THH) is localizing and the
classifications of natural transformations from K to THH.