Johannes Gutenberg Universität Mainz, Deutschland
Weibel's K-dimension conjecture (now a theorem) predicted that the negative K-groups K−i(X) of a noetherian scheme X vanish if i is larger than the Krull dimension of X. In the talk, I will explain a generalization to arbitrary qcqs schemes: K−i(X) vanishes as soon as i is larger than the valuative dimension of the scheme X. The latter notion of dimension equals the Krull dimension in the noetherian case, but is better behaved in the non-noetherian setting. A crucial input is a "derived pro cdh"-descent result which holds in this generality. This is joint work with Shuji Saito and Shane Kelly and also influenced by earlier work with Moritz Kerz and Florian Strunk.