On the K-theory of regular coconnective rings

Abstract

Abstract We show that for a coconnective ring spectrum satisfying regularity and flatness assumptions, its algebraic K-theory agrees with that of its

$$\pi _0$$

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.