On the K-theory of regular coconnective rings

Abstract

AbstractWe show that for a coconnective ring spectrum satisfying regularity and flatness assumptions, its algebraic K-theory agrees with that of its $$\pi _0$$ π 0 . We prove this as a consequence of a more general devissage result for stable infinity categories. Applications of our result include giving general conditions under which K-theory preserves pushouts, generalizations of $$\mathbb {A}^n$$ A n -invariance of K-theory, and an understanding of the K-theory of categories of unipotent local systems.