K-theory and derived equivalences

Duke Mathematical Journal

Volumn 124, Issue 3, 2004, Pages 587-617

  Dugger, Daniel ^a   Shipley, Brooke ^b  

^a UNIVERSITY OF OREGON   (United States)

^b PURDUE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 6344285426     PISSN: 00127094     EISSN: None     Source Type: Journal    
DOI: 10.1215/S0012-7094-04-12435-2     Document Type: Article

References (34)

1. [B] P. BALMER, Presheaves of triangulated categories and reconstruction of schemes, Math. Ann. 324 (2002), 557-580. MR 1938458
2. [BGI] P. BERTHELOT, A. GROTHENDIECK, and L. ILLUSIE, eds., Théorie des intersections et théorème de Riemann-Roch, Séminaire de Géométrie Algébrique du Bois-Marie (SGA 6), Lecture Notes in Math. 225, Springer, Berlin, 1971. MR 0354655
3. [BN] M. BÖKSTEDT and A. NEEMAN, Homotopy limits in triangulated categories, Compositio Math. 86 (1993), 209-234. MR 1214458
4. [Bo] F. BORCEUX, Handbook of Categorical Algebra, II: Categories and Structures, Encyclopedia Math. Appl. 51, Cambridge Univ. Press, Cambridge, 1994. MR 1291599
5. [D] J. DALPAYRAT-GLUTRON, Equivalences dérivées et K-théorie, Mémoire D.E.A., Université Denis Diderot, May 1999.
6. [Du] D. DUGGER, Combinatorial model categories have presentations, Adv. Math. 164 (2001), 177-201. MR 1870516
7. [DS] D. DUGGER and B. SHIPLEY, Stable module categories and differential graded rings, in preparation.
8. [DK] W. G. DWYER and D. M. KAN, Function complexes in homotopical algebra, Topology 19 (1980), 427-440. MR 0584566
9. [DwS] W. G. DWYER and J. SPALINSKI, "Homotopy theories and model categories" in Handbook of Algebraic Topology, North-Holland, Amsterdam, 1995, 73-126. MR 1361887
10. [F] P. FREYD, Abelian Categories: An Introduction to the Theory of Functors, Harper's Ser. in Modern Math., Harper and Row, New York, 1964. MR 0166240
11. [G] P. GABRIEL, Des categories abéliennes, Bull. Soc. Math. France 90 (1962), 323-448. MR 0232821
12. [H] V. HINICH, Homological algebra of homotopy algebras, Comm. Algebra 25 (1997), 3291-3323. MR 1465117
13. [Hi] P. S. HIRSCHHORN, Model Categories and Their Localizations, Math. Surveys Monogr. 99, Amer. Math. Soc., Providence, 2003. MR 1944041
14. [Ho] M. HOVEY, Model Categories, Math. Surveys Monogr. 63, Amer. Math. Soc., Providence, 1999. MR 1650134
15. [HSS] M. HOVEY, B. SHIPLEY, and J. SMITH, Symmetric spectra, J. Amer. Math. Soc. 13 (2000), 149-208. MR 1695653
16. [K] B. KELLER, Deriving DG categories, Ann. Sci. École Norm. Sup. (4) 27 (1994), 63-102. MR 1258406
17. [Ke] G. M. KELLY, Basic Concepts of Enriched Category Theory, London Math. Soc. Lecture Note Ser. 64, Cambridge Univ. Press, Cambridge, 1982. MR 0651714
18. [N1] A. NEEMAN, K-theory for triangulated categories I(A): Homological functors, Asian J. Math. 1 (1997), 330-417. MR 1491990
19. [N2] -, Triangulated Categories, Ann. of Math. Stud. 148, Princeton Univ. Press, Princeton, 2001. MR 1812507
20. [Q1] D. G. QUILLEN, Homotopical Algebra, Lecture Notes in Math. 43, Springer, Berlin, 1967. MR 0223432
21. [Q2] -, "Higher algebraic K-theory, I" in Algebraic K-Theory, I: Higher K-Theories (Seattle, 1972), Lecture Notes in Math. 341, Springer, Berlin, 1973, 85-147. MR 0338129
22. [R1] J. RICKARD, Morita theory for derived categories, J. London Math. Soc. (2) 39 (1989), 436-456. MR 1002456
23. [R2] -, Derived equivalences as derived functors, J. London Math. Soc. (2) 43 (1991), 37-48. MR 1099084
24. [SS1] S. SCHWEDE and B. E. SHIPLEY, Algebras and modules in monoidal model categories, Proc. London Math. Soc. (3) 80 (2000), 491-511. MR 1734325
25. [SS2] -, Equivalences of monoidal model categories, Algebr. Geom. Topol. 3 (2003), 287-334. MR 1997322
26. [SS3] -, Stable model categories are categories of modules, Topology 42 (2003), 103-153. MR 1928647
27. [S] M. SCHLICHTING, A note on K-theory and triangulated categories, Invent. Math. 150 (2002), 111-116. MR 1930883
28. [Se] G. SEGAL, Classifying spaces and spectral sequences, Inst. Hautes Études Sci. Publ. Math. 34 (1968), 105-112. MR 0232393
29. 1- equivariant homotopy theory, Q. J. Math. 53 (2002), 87-110. MR 1887672
30. [Sr] V. SRINIVAS, Algebraic K-Theory, 2nd ed., Progr. Math. 90, Birkhäuser, Boston, 1996. MR 1382659
31. [TT] R. W. THOMASON and T. TROBAUGH, "Higher algebraic K-theory of schemes and of derived categories" in The Grothendieck Festschrift, Vol. III, Progr. Math. 88, Birkhäuser, Boston, 1990, 247-435. MR 1106918
32. [TV] B. TOËN and G. VEZZOSI, A remark on K-theory and S-categories, Topology 43 (2004), 765-791. MR 2061207
33. [W] F. WALDHAUSEN, "Algebraic K-theory of spaces" in Algebraic and Geometric Topology (New Brunswick, N.J., 1983), Lecture Notes in Math. 1126, Springer, Berlin, 1985, 318-419. MR 0802796
34. [We] C. WEIBEL, An Introduction to Homological Algebra, Cambridge Stud. Adv. Math. 38, Cambridge Univ. Press, Cambridge, 1994. MR 1269324