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

Dugger, Daniel; Shipley, Brooke

doi:10.2140/agt.2009.9.135

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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

DOI: 10.2140/agt.2009.9.135

Abstract

The paper gives a new proof that the model categories of stable modules for the rings $ℤ ∕ p^{2}$ and $ℤ ∕ p [ϵ] ∕ (ϵ^{2})$ 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

References

Publication

Received: 12 June 2008

Revised: 17 December 2008

Accepted: 16 December 2008

Published: 25 January 2009

Authors

Daniel Dugger
University of Oregon Department of Mathematics Eugene, OR 97403 USA

Brooke Shipley
Department of Mathematics Statistics and Computer Science 508 SEO (m/c 249) 851 S. Morgan St. Chicago, IL 60607-7045 USA
http://www.math.uic.edu/~bshipley/

Volume 9, issue 1 (2009)