$c$-structures and trace methods beyond connective rings
K-Theory and Homology
2025-09-19 v1 Algebraic Geometry
Algebraic Topology
Category Theory
Abstract
We introduce the notion of a -category, which is a kind of category whose behaviour is controlled by connective ring spectra. More precisely, any -category admits a finite step resolution by categories of compact modules over connective ring spectra. We introduce nilpotent extensions of -categories, and show that they induce isomorphisms on truncating invariants, such as the fiber of the cyclotomic trace map. We show that for many stacks, the category of perfect complexes is naturally a -category and deduce a generalization of the Dundas--Goodwillie--McCarthy theorem to such stacks.
Cite
@article{arxiv.2509.14774,
title = {$c$-structures and trace methods beyond connective rings},
author = {Ishan Levy and Vladimir Sosnilo},
journal= {arXiv preprint arXiv:2509.14774},
year = {2025}
}