Geometry & Topology Volume 16, issue 2 (2012)

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

Author Index

To Appear

Other MSP Journals

Localization theorems in topological Hochschild homology and topological cyclic homology

Andrew J Blumberg and Michael A Mandell

Geometry & Topology 16 (2012) 1053–1120

DOI: 10.2140/gt.2012.16.1053

Bibliography

1	S Bloch, S Lichtenbaum, A spectral sequence for motivic cohomology, preprint (1995)
2	A J Blumberg, M A Mandell, Algebraic $K$–theory and abstract homotopy theory, Adv. Math. 226 (2011) 3760 MR2764905
3	M Bökstedt, Topological Hochschild homology, Bielefeld preprint (1988)
4	M Bökstedt, W C Hsiang, I Madsen, The cyclotomic trace and algebraic $K$–theory of spaces, Invent. Math. 111 (1993) 465 MR1202133
5	A I Bondal, M Larsen, V A Lunts, Grothendieck ring of pretriangulated categories, Int. Math. Res. Not. 2004 (2004) 1461 MR2051435
6	A K Bousfield, The localization of spaces with respect to homology, Topology 14 (1975) 133 MR0380779
7	G Cortiñas, Infinitesimal $K$–theory, J. Reine Angew. Math. 503 (1998) 129 MR1650347
8	G Cortiñas, C Haesemeyer, M Schlichting, C Weibel, Cyclic homology, cdh-cohomology and negative $K$–theory, Ann. of Math. 167 (2008) 549 MR2415380
9	G Cortiñas, C Haesemeyer, C Weibel, $K$–regularity, $cdh$–fibrant Hochschild homology, and a conjecture of Vorst, J. Amer. Math. Soc. 21 (2008) 547 MR2373359
10	V Drinfeld, DG quotients of DG categories, J. Algebra 272 (2004) 643 MR2028075
11	D Dugger, Spectral enrichments of model categories, Homology, Homotopy Appl. 8 (2006) 1 MR2205213
12	D Dugger, B Shipley, Enriched model categories and an application to additive endomorphism spectra, Theory Appl. Categ. 18 (2007) 400 MR2342167
13	B I Dundas, R McCarthy, Topological Hochschild homology of ring functors and exact categories, J. Pure Appl. Algebra 109 (1996) 231 MR1388700
14	A D Elmendorf, I Kriz, M A Mandell, J P May, Rings, modules, and algebras in stable homotopy theory, Math.Surveys and Monogr. 47, Amer. Math. Soc. (1997) MR1417719
15	E M Friedlander, A Suslin, The spectral sequence relating algebraic $K$–theory to motivic cohomology, Ann. Sci. École Norm. Sup. 35 (2002) 773 MR1949356
16	T Geisser, L Hesselholt, Topological cyclic homology of schemes, from: "Algebraic $K$–theory (Seattle, WA, 1997)" (editors W Raskind, C Weibel), Proc. Sympos. Pure Math. 67, Amer. Math. Soc. (1999) 41 MR1743237
17	T Geisser, L Hesselholt, On the vanishing of negative $K$–groups, Math. Ann. 348 (2010) 707 MR2677901
18	T G Goodwillie, Relative algebraic $K$–theory and cyclic homology, Ann. of Math. 124 (1986) 347 MR855300
19	L Hesselholt, I Madsen, Cyclic polytopes and the $K$–theory of truncated polynomial algebras, Invent. Math. 130 (1997) 73 MR1471886
20	L Hesselholt, I Madsen, On the $K$–theory of finite algebras over Witt vectors of perfect fields, Topology 36 (1997) 29 MR1410465
21	L Hesselholt, I Madsen, On the $K$–theory of local fields, Ann. of Math. 158 (2003) 1 MR1998478
22	P S Hirschhorn, Model categories and their localizations, Math. Surveys and Monogr. 99, Amer. Math. Soc. (2003) MR1944041
23	M Hovey, J H Palmieri, N P Strickland, Axiomatic stable homotopy theory, Amer. Math. Soc. (1997) MR1388895
24	M Hovey, B Shipley, J Smith, Symmetric spectra, J. Amer. Math. Soc. 13 (2000) 149 MR1695653
25	B Keller, On the cyclic homology of exact categories, J. Pure Appl. Algebra 136 (1999) 1 MR1667558
26	G M Kelly, Basic concepts of enriched category theory, London Math. Soc. Lecture Note Series 64, Cambridge Univ. Press (1982) 245 MR651714
27	T A Kro, Model structure on operads in orthogonal spectra, Homology, Homotopy Appl. 9 (2007) 397 MR2366955
28	M Levine, The homotopy coniveau tower, J. Topol. 1 (2008) 217 MR2365658
29	L G Lewis Jr., Is there a convenient category of spectra?, J. Pure Appl. Algebra 73 (1991) 233 MR1124786
30	L G Lewis Jr., J P May, M Steinberger, J E McClure, Equivariant stable homotopy theory, Lecture Notes in Math. 1213, Springer (1986) MR866482
31	M A Mandell, J P May, Equivariant orthogonal spectra and $S$–modules, Amer. Math. Soc. (2002) MR1922205
32	M A Mandell, J P May, S Schwede, B Shipley, Model categories of diagram spectra, Proc. London Math. Soc. 82 (2001) 441 MR1806878
33	J P May, The geometry of iterated loop spaces, Lectures Notes in Math. 271, Springer (1972) MR0420610
34	J P May, Equivariant homotopy and cohomology theory, CBMS Regional Conference Series in Math. 91, Conference Board of the Math. Sciences (1996) MR1413302
35	R McCarthy, Relative algebraic $K$–theory and topological cyclic homology, Acta Math. 179 (1997) 197 MR1607555
36	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. 25 (1992) 547 MR1191736
37	S Schwede, B Shipley, Equivalences of monoidal model categories, Algebr. Geom. Topol. 3 (2003) 287 MR1997322
38	S Schwede, B Shipley, Stable model categories are categories of modules, Topology 42 (2003) 103 MR1928647
39	B Shipley, Symmetric spectra and topological Hochschild homology, $K$–Theory 19 (2000) 155 MR1740756
40	B Shipley, $H\mathbb Z$–algebra spectra are differential graded algebras, Amer. J. Math. 129 (2007) 351 MR2306038
41	R W Thomason, Algebraic $K$–theory and étale cohomology, Ann. Sci. École Norm. Sup. 18 (1985) 437 MR826102
42	R W Thomason, Les $K$–groupes d'un schéma éclaté et une formule d'intersection excédentaire, Invent. Math. 112 (1993) 195 MR1207482
43	R W Thomason, T Trobaugh, Higher algebraic $K$–theory of schemes and of derived categories, from: "The Grothendieck Festschrift, Vol. III" (editors P Cartier, L Illusie, N M Katz, G Laumon, K A Ribet), Progr. Math. 88, Birkhäuser (1990) 247 MR1106918
44	B Toën, G Vezzosi, A remark on $K$–theory and $S$–categories, Topology 43 (2004) 765 MR2061207
45	F Waldhausen, Algebraic $K$–theory of topological spaces. II, from: "Algebraic topology, Aarhus 1978 (Proc. Sympos., Univ. Aarhus, 1978)" (editors J L Dupont, I H Madsen), Lecture Notes in Math. 763, Springer (1979) 356 MR561230
46	F Waldhausen, Algebraic $K$–theory of spaces, from: "Algebraic and geometric topology (New Brunswick, NJ, 1983)" (editors A Ranicki, N Levitt, F Quinn), Lecture Notes in Math. 1126, Springer (1985) 318 MR802796