K-theory for triangulated categories 3 3/4: A direct proof of the theorem of the heart

K-Theory

Volumn 22, Issue 1-2, 2001, Pages 1-144

  Neeman, Amnon ^a  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

Author keywords

K theory; Simplicial sets; Triangulated categories

Indexed keywords

EID: 0013129203     PISSN: 09203036     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1011172502978     Document Type: Article

References (23)

1. Beilinson, A. A., Bernstein, J. and Deligne, P.: Analyse et topologie sur les éspaces singuliers, Astérisque 100, Soc. Math. France (1982).
2. Borel, A. and Serre, J. P.: Le théorème de Riemann-Roch, Bull. Soc. Math. France 86 (1958), 97-136.
3. Giffen, C. and Neeman, A.: K-theory for triangulated categories, Preprint.
4. Hartshorne, R.: Residues and Duality, Lecture Notes in Math. 20, Springer, New York, 1966.
5. Hinich, V. A. and Schechtman, V. V.: Geometry of a category of complexes and algebraic K-theory, Duke Math. J. 52 (1985), 399-430.
6. Jardine, J. F.: The multiple Q-constructions, Canad. J. Math. 39 (1987), 1174-1209.
7. Neeman, A.: Some new axioms for triangulated categories, J. Algebra 139 (1991), 221-255.
8. Neeman, A.: The Brown representability theorem and phantomless triangulated categories, J. Algebra 151 (1992), 118-155.
9. Neeman, A.: K-theory for triangulated categories I(A): homological functors, Asian J. Math. 1 (1997), 330-417.
10. Neeman, A.: K-theory for triangulated categories I(B): homological functors, Asian J. Math. 1 (1997), 435-519.
11. Neeman, A.: K-theory for triangulated categories II: the subtlety of the theory and potential pitfalls, Asian J. Math. 2 (1998), 1-125.
12. Neeman, A.: K-theory for triangulated categories III(A): the theorem of the heart, Asian J. Math. 2 (1998), 495-589.
13. Neeman, A.: K-theory for triangulated categories III(B): the theorem of the heart, Asian J. Math. 3 (1999), 557-608.
14. Neeman, A.: K-theory for triangulated categories 3 1/2(A): a detailed proof of the theorem of homological functors, K-Theory 20 (2000), 97-174.
15. Neeman, A.: K-theory for triangulated categories 3 1/2(B): a detailed proof of the theorem of homological functors, K-Theory 20 (2000), 243-298.
16. Neeman, A. and Retakh, V.: Extension categories and their homotopy, Preprint.
17. Quillen, D.: Higher algebraic K-theory I, In: Lecture Notes in Math. 341, Springer, New York, 1973, pp. 85-147.
18. Segal, G.: Categories and cohomology theories, Topology 13 (1974), 293-312.
19. Thomason, R. and Trobaugh, T.: Higher algebraic K-theory of schemes and of derived categories. In: The Grothendieck Festschrift (a collection of papers to honor Grothendieck's 60th birthday) Volume 3, Birkhäuser, Basel, 1990, pp. 247-435.
20. Vaknin, A.: Virtual triangles, Preprint, 1999.
21. Verdier, J. L.: Catégories dérivées, état 0. SGA 4 1/2, In: Lecture Notes in Math. 569, Springer, New York, 1977, pp. 262-308.
22. Waldhausen, F.: Algebraic K-theory of generalized free products I, II. Ann. of Math. 108 (1978), 135-256.
23. Waldhausen, F.: Algebraic K-theory of spaces, In: Lecture Notes in Math. 1126, Springer, New York, 1985, pp. 318-419.