Algebraic K-theory and abstract homotopy theory

We decompose the K-theory space of a Waldhausen category in terms of its Dwyer-Kan simplicial localization. This leads to a criterion for functors to induce equivalences of K-theory spectra that generalizes and explains many of the criteria appearing in the literature. We show that under mild hypotheses, a weakly exact functor that induces an equivalence of homotopy categories induces an equivalence of K-theory spectra.Comment: Final versio

The strong K\"unneth theorem for topological periodic cyclic homology

Topological periodic cyclic homology (i.e., $\mathbb{T}$-Tate of $THH$) has the structure of a strong symmetric monoidal functor of smooth and proper dg categories over a perfect field of finite characteristic