Geometry & Topology Volume 8, issue 3 (2004)

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ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

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Noncommutative localisation in algebraic $K$–theory I

Amnon Neeman and Andrew Ranicki

Geometry & Topology 8 (2004) 1385–1425

DOI: 10.2140/gt.2004.8.1385

Bibliography

1	H Bass, Algebraic $K$–theory, W. A. Benjamin, New York-Amsterdam (1968) MR0249491
2	A A Beĭlinson, J Bernstein, P Deligne, Faisceaux pervers, from: "Analysis and topology on singular spaces I (Luminy, 1981)", Astérisque 100, Soc. Math. France (1982) 5 MR751966
3	G M Bergman, W Dicks, Universal derivations and universal ring constructions, Pacific J. Math. 79 (1978) 293 MR531320
4	M Bökstedt, A Neeman, Homotopy limits in triangulated categories, Compositio Math. 86 (1993) 209 MR1214458
5	A K Bousfield, The localization of spaces with respect to homology, Topology 14 (1975) 133 MR0380779
6	A K Bousfield, The localization of spectra with respect to homology, Topology 18 (1979) 257 MR551009
7	P M Cohn, Free rings and their relations, London Mathematical Society Monographs 2, Academic Press (1971) MR0371938
8	W Dicks, Mayer–Vietoris persentations over colimits of rings, Proc. London Math. Soc. $(3)$ 34 (1977) 557 MR0444709
9	M Farber, A Ranicki, The Morse–Novikov theory of circle-valued functions and noncommutative localization, Tr. Mat. Inst. Steklova 225 (1999) 381 MR1725953
10	M Farber, P Vogel, The Cohn localization of the free group ring, Math. Proc. Cambridge Philos. Soc. 111 (1992) 433 MR1151322
11	W Geigle, H Lenzing, Perpendicular categories with applications to representations and sheaves, J. Algebra 144 (1991) 273 MR1140607
12	H Gillet, Riemann–Roch theorems for higher algebraic $K$–theory, Adv. in Math. 40 (1981) 203 MR624666
13	D Grayson, Higher algebraic $K$–theory II (after Daniel Quillen), from: "Algebraic $K$–theory (Proc. Conf., Northwestern Univ., Evanston, Ill., 1976)", Springer (1976) MR0574096
14	D R Grayson, $K$–theory and localization of noncommutative rings, J. Pure Appl. Algebra 18 (1980) 125 MR585217
15	D R Grayson, Exact sequences in algebraic $K$–theory, Illinois J. Math. 31 (1987) 598 MR909785
16	B Keller, Deriving DG categories, Ann. Sci. École Norm. Sup. $(4)$ 27 (1994) 63 MR1258406
17	B Keller, A remark on the generalized smashing conjecture, Manuscripta Math. 84 (1994) 193 MR1285956
18	H Krause, Smashing subcategories and the telescope conjecture—an algebraic approach, Invent. Math. 139 (2000) 99 MR1728877
19	H Krause, Cohomological quotients and smashing localizations, Amer. J. Math. 127 (2005) 1191 MR2183523
20	M Levine, Localization on singular varieties, Invent. Math. 91 (1988) 423 MR928491
21	A Neeman, The chromatic tower for $D(R)$, Topology 31 (1992) 519 MR1174255
22	A Neeman, The connection between the $K$–theory localization theorem of Thomason, Trobaugh and Yao and the smashing subcategories of Bousfield and Ravenel, Ann. Sci. École Norm. Sup. $(4)$ 25 (1992) 547 MR1191736
23	A Neeman, Triangulated categories, Annals of Mathematics Studies 148, Princeton University Press (2001) MR1812507
24	A Neeman, Non-compactly generated categories, Topology 37 (1998) 981 MR1650410
25	A Neeman, A Ranicki, Noncommutative localization and chain complexes I: Algebraic $K$– and $L$–theory arXiv:math.RA/0109118
26	A Neeman, A Ranicki, Noncommutative localisation in algebraic $K$–theory II
27	A Neeman, A Ranicki, Noncommutative localisation in algebraic $K$–theory
28	A Neeman, A Ranicki, A Schofield, Representations of algebras as universal localizations, Math. Proc. Cambridge Philos. Soc. 136 (2004) 105 MR2034017
29	D Quillen, Higher algebraic $K$–theory I, from: "Algebraic $K$–theory, I: Higher $K$–theories (Proc. Conf., Battelle Memorial Inst., Seattle, Wash., 1972)", Springer (1973) MR0338129
30	A Ranicki, High-dimensional knot theory, Springer Monographs in Mathematics, Springer (1998) MR1713074
31	A Ranicki, Noncommutative localization in topology, from: "Non-commutative localization in algebra and topology", London Math. Soc. Lecture Note Ser. 330, Cambridge Univ. Press (2006) 81 MR2222483
32	J Rickard, Morita theory for derived categories, J. London Math. Soc. $(2)$ 39 (1989) 436 MR1002456
33	A H Schofield, Representation of rings over skew fields, London Mathematical Society Lecture Note Series 92, Cambridge University Press (1985) MR800853
34	N Spaltenstein, Resolutions of unbounded complexes, Compositio Math. 65 (1988) 121 MR932640
35	R W Thomason, T Trobaugh, Higher algebraic $K$–theory of schemes and of derived categories, from: "The Grothendieck Festschrift, Vol. III", Progr. Math. 88, Birkhäuser (1990) 247 MR1106918
36	P Vogel, Localization in algebraic $L$–theory, from: "Topology Symposium, Siegen 1979 (Proc. Sympos., Univ. Siegen, Siegen, 1979)", Lecture Notes in Math. 788, Springer (1980) 482 MR585677
37	P Vogel, On the obstruction group in homology surgery, Inst. Hautes Études Sci. Publ. Math. (1982) 165 MR672183
38	F Waldhausen, Algebraic $K$–theory of spaces, from: "Algebraic and geometric topology (New Brunswick, N.J., 1983)", Lecture Notes in Math. 1126, Springer (1985) 318 MR802796
39	C A Weibel, Negative $K$–theory of varieties with isolated singularities, from: "Proceedings of the Luminy conference on algebraic $K$–theory (Luminy, 1983)" (1984) 331 MR772067
40	C A Weibel, A Brown–Gersten spectral sequence for the $K$–theory of varieties with isolated singularities, Adv. in Math. 73 (1989) 192 MR987274
41	C Weibel, D Yao, Localization for the $K$–theory of noncommutative rings, from: "Algebraic $K$–theory, commutative algebra, and algebraic geometry (Santa Margherita Ligure, 1989)", Contemp. Math. 126, Amer. Math. Soc. (1992) 219 MR1156514
42	D Yao, Higher algebraic $K$–theory of admissible abelian categories and localization theorems, J. Pure Appl. Algebra 77 (1992) 263 MR1154705