Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 12, Number 4 (2012), 2329-2388.
On the algebraic classification of module spectra
Using methods developed by Franke in [K-theory Preprint Archives 139 (1996)], we obtain algebraic classification results for modules over certain symmetric ring spectra (S-algebras). In particular, for any symmetric ring spectrum whose graded homotopy ring has graded global homological dimension and is concentrated in degrees divisible by some natural number , we prove that the homotopy category of –modules is equivalent to the derived category of the homotopy ring . This improves the Bousfield-Wolbert algebraic classification of isomorphism classes of objects of the homotopy category of R-modules. The main examples of ring spectra to which our result applies are the –local real connective –theory spectrum , the Johnson–Wilson spectrum , and the truncated Brown–Peterson spectrum , all for an odd prime . We also show that the equivalences for all these examples are exotic in the sense that they do not come from a zigzag of Quillen equivalences.
Algebr. Geom. Topol., Volume 12, Number 4 (2012), 2329-2388.
Received: 4 November 2011
Revised: 19 July 2012
Accepted: 19 July 2012
First available in Project Euclid: 19 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 18E30: Derived categories, triangulated categories 55P42: Stable homotopy theory, spectra 55P43: Spectra with additional structure ($E_\infty$, $A_\infty$, ring spectra, etc.)
Secondary: 18G55: Homotopical algebra
Patchkoria, Irakli. On the algebraic classification of module spectra. Algebr. Geom. Topol. 12 (2012), no. 4, 2329--2388. doi:10.2140/agt.2012.12.2329. https://projecteuclid.org/euclid.agt/1513715460