On the K-theory of regular coconnective rings

TL;DR

This paper proves that for certain regular coconnective ring spectra, their algebraic K-theory matches that of their zeroth homotopy group, with broad implications for K-theory invariance and applications.

Contribution

It establishes a general devissage result linking K-theory of ring spectra to their π₀, extending understanding of K-theory invariance and behavior under pushouts.

Findings

K-theory of regular coconnective ring spectra equals that of π₀.

K-theory preserves pushouts under certain conditions.

Generalizes A^n-invariance of K-theory.

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.