# Thomas Kragh: Non-connective K-theory

**Time: **
Fri 2020-06-26 10.15 - 12.00

**Location: **
Zoom ID 624 1309 9107

**Participating: **
Thomas Kragh

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.

Zoom password: 528897