Work

Quivers and the Adams spectral sequence

Year: 2025

Type: article

Abstract: In this paper, we describe a novel way of identifying Adams spectral sequence $E_2$-terms in terms of homological algebra of quiver representations. Our method applies much more broadly than the standard techniques based on descent-flatness, bearing on a varied array of ring spectra. In the particular case of $p$-local integral homology, we are able to give a decomposition of the $E_2$-term, describing it completely in terms of the classical Adams spectral sequence. In the appendix, which can be read independently from the main body of the text, we develop functoriality of deformations of $\infty$-categories of the second author and Patchkoria.

Source: Advances in Mathematics

DOI: 10.1016/j.aim.2025.110270

Authors: Robert Burklund, Piotr Pstrągowski

Institution: University of Copenhagen

Language: English

Topic: Homotopy and Cohomology in Algebraic Topology

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,790

Funders: National Science Foundation, National Research Foundation, Deutsche Forschungsgemeinschaft, Danmarks Grundforskningsfond