Homology, Homotopy and Applications

Volume 23 (2021)

Number 1

Flatness and Shipley’s algebraicization theorem

Pages: 191 – 218

DOI: https://dx.doi.org/10.4310/HHA.2021.v23.n1.a11


Jordan Williamson (School of Mathematics and Statistics, Sheffield, United Kingdom)


We provide an enhancement of Shipley’s algebraicization theorem which behaves better in the context of commutative algebras. This involves defining flat model structures as in Shipley and Pavlov–Scholbach, and showing that the functors still provide Quillen equivalences in this refined context. The use of flat model structures allows one to identify the algebraic counterparts of change of groups functors, as demonstrated in forthcoming work of the author.


flat model structure, commutative algebra spectra, rational algebraic models

2010 Mathematics Subject Classification


Received 18 January 2020

Received revised 16 June 2020

Accepted 29 June 2020

Published 2 September 2020