Volume 9, issue 1 (2009)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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 p2 and p[ϵ](ϵ2) 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/