The Multiplication on BP

BP is an E_4 ring spectrum. The E_4 structure is unique up to automorphism

Modules in Monoidal Model Categories

This paper studies the existence of and compatibility between derived change of ring, balanced product, and function module derived functors on module categories in monoidal model categories

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

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