On the K-theory of regular coconnective rings

Abstract

We show that for a coconnective ring spectrum satisfying regularity and flatness assumptions, its algebraic K-theory agrees with that of its $\pi_0$. 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 $\mathbb{A}^n$-invariance of K-theory, and an understanding of the K-theory of categories of unipotent local systems.