Volume 9, issue 1 (2009)

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A curious example of triangulated-equivalent model categories which are not Quillen equivalent

Daniel Dugger and Brooke Shipley

Algebraic & Geometric Topology 9 (2009) 135–166
Abstract

The paper gives a new proof that the model categories of stable modules for the rings $ℤ∕{p}^{2}$ and $ℤ∕p\left[ϵ\right]∕\left({ϵ}^{2}\right)$ are not Quillen equivalent. The proof uses homotopy endomorphism ring spectra. Our considerations lead to an example of two differential graded algebras which are derived equivalent but whose associated model categories of modules are not Quillen equivalent. As a bonus, we also obtain derived equivalent dgas with non-isomorphic $K$–theories.

Keywords
model categories, stable module category, differential graded algebras
Mathematical Subject Classification 2000
Primary: 18E30, 18F25, 55U35