English

On the K-theory of regular coconnective rings

K-Theory and Homology 2021-12-30 v1 Algebraic Topology

Abstract

We show that for a coconnective ring spectrum satisfying regularity and flatness assumptions, its algebraic K-theory agrees with that of its π0\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 An\mathbb{A}^n-invariance of K-theory, and an understanding of the K-theory of categories of unipotent local systems.

Keywords

Cite

@article{arxiv.2112.14723,
  title  = {On the K-theory of regular coconnective rings},
  author = {Robert Burklund and Ishan Levy},
  journal= {arXiv preprint arXiv:2112.14723},
  year   = {2021}
}

Comments

24 pages. Comments welcome!