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2012 On the algebraic classification of module spectra
Irakli Patchkoria
Algebr. Geom. Topol. 12(4): 2329-2388 (2012). DOI: 10.2140/agt.2012.12.2329

Abstract

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 R whose graded homotopy ring πR has graded global homological dimension 2 and is concentrated in degrees divisible by some natural number N4, we prove that the homotopy category of R–modules is equivalent to the derived category of the homotopy ring πR. 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 p–local real connective K–theory spectrum ko(p), the Johnson–Wilson spectrum E(2), and the truncated Brown–Peterson spectrum BP1, all for an odd prime p. 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.

Citation

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Irakli Patchkoria. "On the algebraic classification of module spectra." Algebr. Geom. Topol. 12 (4) 2329 - 2388, 2012. https://doi.org/10.2140/agt.2012.12.2329

Information

Received: 4 November 2011; Revised: 19 July 2012; Accepted: 19 July 2012; Published: 2012
First available in Project Euclid: 19 December 2017

zbMATH: 1264.18017
MathSciNet: MR3020210
Digital Object Identifier: 10.2140/agt.2012.12.2329

Subjects:
Primary: 18E30, 55P42, 55P43
Secondary: 18G55

Rights: Copyright © 2012 Mathematical Sciences Publishers

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Vol.12 • No. 4 • 2012
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