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Endofiniteness in stable homotopy theory

Authors: Henning Krause and Ulrike Reichenbach
Journal: Trans. Amer. Math. Soc. 353 (2001), 157-173
MSC (2000): Primary 55P42, 55U35
Published electronically: June 20, 2000
MathSciNet review: 1783792
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Abstract: We study endofinite objects in a compactly generated triangulated category in terms of ideals in the category of compact objects. Our results apply in particular to the stable homotopy category. This leads, for example, to a new interpretation of stable splittings for classifying spaces of finite groups.

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  • 1. J.F. ADAMS, Stable homotopy and generalised homology, The University of Chicago Press (1974). MR 53:6534
  • 2. G. CARLSSON, Equivariant stable homotopy and Segal's Burnside ring conjecture, Ann. Math. 120 (1984), 189-224. MR 86f:57036
  • 3. W.W. CRAWLEY-BOEVEY, Modules of finite length over their endomorphism ring, in: Representations of algebras and related topics, eds. S. Brenner and H. Tachikawa, London Math. Soc. Lec. Note Series 168 (1992), 127-184. MR 94h:16018
  • 4. W.W. CRAWLEY-BOEVEY, Locally finitely presented additive categories, Comm. Algebra 22 (1994), 1641-1674. MR 95h:18009
  • 5. A.D. ELMENDORF AND I. KRIZ AND M.A. MANDELL AND J.P. MAY, Rings, modules, and algebras in stable homotopy theory, Amer. Math. Soc., Mathematical Surveys and Monographs 47 (1997). MR 97h:55006
  • 6. P. FREYD, Stable homotopy, in: Proceedings of the conference on categorical algebra, La Jolla, Springer-Verlag, New York (1966), 121-172. MR 35:2280
  • 7. P. GABRIEL, Des catégories abéliennes, Bull. Soc. Math. France 90 (1962), 323-448. MR 38:1144
  • 8. L. GRUSON AND C.U. JENSEN, Deux applications de la notion de $L$-dimension, C. R. Acad. Sci. Paris Ser. A 282 (1976), 23-24. MR 53:5706
  • 9. H.-W. HENN, Finiteness properties of injective resolutions of certain unstable modules over the Steenrod algebra and applications, Math. Ann. 291 (1991), 191-203. MR 92i:55016
  • 10. M. HOVEY, J.H. PALMIERI, N.P. STRICKLAND, Axiomatic stable homotopy theory, Mem. Amer. Math. Soc. 610 (1997). MR 98a:55017
  • 11. C.U. JENSEN AND H. LENZING, Model theoretic algebra, Gordon and Breach, New York (1989). MR 91m:03038
  • 12. H. KRAUSE, The spectrum of a locally coherent category, J. Pure Appl. Algebra 114 (1997), 259-271. MR 98e:18006
  • 13. H. KRAUSE, Exactly definable categories, J. Algebra 201 (1998), 456-492. MR 99j:18010
  • 14. H. KRAUSE, Smashing subcategories and the telescope conjecture - an algebraic approach, Invent. Math. 139 (2000), 99-133. CMP 2000:06
  • 15. H. KRAUSE, Decomposing thick subcategories of the stable module category, Math. Ann. 313 (1999), 95-108. CMP 99:07
  • 16. H.R. MARGOLIS, Spectra and the Steenrod algebra, North-Holland (1983). MR 86j:55001
  • 17. A. NEEMAN, The Grothendieck duality theorem via Bousfield's techniques and Brown representability, J. Amer. Math. Soc. 9 (1996), 205-236. MR 96c:18006
  • 18. J.L. VERDIER, Catégories derivées, état 0, SGA $4\tfrac12$, Springer Lec. Notes 569 (1977), 262-311. MR 57:3132

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Additional Information

Henning Krause
Affiliation: Fakultät für Mathematik, Universität Bielefeld, 33501 Bielefeld, Germany

Ulrike Reichenbach
Affiliation: Fakultät für Mathematik, Universität Bielefeld, 33501 Bielefeld, Germany

Received by editor(s): November 18, 1998
Published electronically: June 20, 2000
Article copyright: © Copyright 2000 American Mathematical Society

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