Volume 16 (2009)

Download this article
For screen
For printing
Recent Volumes
Volume 1, 1998
Volume 2, 1999
Volume 3, 2000
Volume 4, 2002
Volume 5, 2002
Volume 6, 2003
Volume 7, 2004
Volume 8, 2006
Volume 9, 2006
Volume 10, 2007
Volume 11, 2007
Volume 12, 2007
Volume 13, 2008
Volume 14, 2008
Volume 15, 2008
Volume 16, 2009
Volume 17, 2011
Volume 18, 2012
Volume 19, 2015
The Series
MSP Books and Monographs
About this Series
Editorial Board
Ethics Statement
Author Index
Submission Guidelines
Author Copyright Form
ISSN (electronic): 1464-8997
ISSN (print): 1464-8989
Other MSP Publications

Topological logarithmic structures

John Rognes

Geometry & Topology Monographs 16 (2009) 401–544

DOI: 10.2140/gtm.2009.16.401

1 V Angeltveit, Topological Hochschild homology and cohomology of A ring spectra, Geom. Topol. 12 (2008) 987–1032 MR2403804
2 V Angeltveit, J Rognes, Hopf algebra structure on topological Hochschild homology, Algebr. Geom. Topol. 5 (2005) 1223–1290 MR2171809
3 C Ausoni, On the algebraic K–theory of the complex K–theory spectrum arXiv:0902.2334
4 C Ausoni, Topological Hochschild homology of connective complex K–theory, Amer. J. Math. 127 (2005) 1261–1313 MR2183525
5 C Ausoni, J Rognes, Algebraic K–theory of topological K–theory, Acta Math. 188 (2002) 1–39 MR1947457
6 C Ausoni, J Rognes, Rational algebraic K–theory of topological K–theory arXiv:0708.2160
7 C Ausoni, J Rognes, Algebraic K–theory of the fraction field of topological K–theory, in preparation
8 N A Baas, B I Dundas, B Richter, J Rognes, Ring completion of rig categories arXiv:0706.0531
9 N A Baas, B I Dundas, B Richter, J Rognes, Stable bundles over rig categories arXiv:0706.0531
10 N A Baas, B I Dundas, J Rognes, Two-vector bundles and forms of elliptic cohomology, from: "Topology, geometry and quantum field theory" (editor U Tillman), London Math. Soc. Lecture Note Ser. 308, Cambridge Univ. Press (2004) 18–45 MR2079370
11 A Baker, H Gilmour, P Reinhard, Topological André–Quillen homology for cellular commutative S–algebras, Abhand. Math. Sem. Univ. Hamburg 78 (2008) 27–50
12 M Basterra, André–Quillen cohomology of commutative S–algebras, J. Pure Appl. Algebra 144 (1999) 111–143 MR1732625
13 M Basterra, M A Mandell, Homology and cohomology of E ring spectra, Math. Z. 249 (2005) 903–944 MR2126222
14 A J Blumberg, M A Mandell, The localization sequence for the algebraic K–theory of topological K–theory, Acta Math. 200 (2008) 155–179 MR2413133
15 M Bökstedt, W C Hsiang, I Madsen, The cyclotomic trace and algebraic K–theory of spaces, Invent. Math. 111 (1993) 465–539 MR1202133
16 A K Bousfield, E M Friedlander, Homotopy theory of Γ –spaces, spectra, and bisimplicial sets, from: "Geometric applications of homotopy theory (Proc. Conf., Evanston, Ill., 1977), II", Lecture Notes in Math. 658, Springer (1978) 80–130 MR513569
17 M Brun, Z Fiedorowicz, R M Vogt, On the multiplicative structure of topological Hochschild homology, Algebr. Geom. Topol. 7 (2007) 1633–1650 MR2366174
18 F R Cohen, T J Lada, J P May, The homology of iterated loop spaces, Lecture Notes in Math. 533, Springer (1976) MR0436146
19 F R Cohen, M E Mahowald, R J Milgram, The stable decomposition for the double loop space of a sphere, from: "Algebraic and geometric topology (Proc. Sympos. Pure Math., Stanford Univ., 1976), Part 2" (editor R J Milgram), Proc. Sympos. Pure Math., XXXII, Amer. Math. Soc. (1978) 225–228 MR520543
20 W Dwyer, E Friedlander, V Snaith, R Thomason, Algebraic K–theory eventually surjects onto topological K–theory, Invent. Math. 66 (1982) 481–491 MR662604
21 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 With an appendix by M Cole
22 F T Farrell, L E Jones, Stable pseudoisotopy spaces of compact non-positively curved manifolds, J. Differential Geom. 34 (1991) 769–834 MR1139646
23 V Franjou, T Pirashvili, On the Mac Lane cohomology for the ring of integers, Topology 37 (1998) 109–114 MR1480880
24 E M Friedlander, B Mazur, Filtrations on the homology of algebraic varieties, Mem. Amer. Math. Soc. 110, Amer. Math. Soc. (1994) MR1211371 With an appendix by D Quillen
25 E Getzler, M M Kapranov, Cyclic operads and cyclic homology, from: "Geometry, topology, & physics" (editor S T Yau), Conf. Proc. Lecture Notes Geom. Topology, IV, Int. Press (1995) 167–201 MR1358617
26 K Hagihara, Structure theorem of Kummer étale K–group, K–Theory 29 (2003) 75–99 MR2029756
27 L Hesselholt, On the p–typical curves in Quillen's K–theory, Acta Math. 177 (1996) 1–53 MR1417085
28 L Hesselholt, I Madsen, On the K–theory of finite algebras over Witt vectors of perfect fields, Topology 36 (1997) 29–101 MR1410465
29 L Hesselholt, I Madsen, On the K–theory of local fields, Ann. of Math. (2) 158 (2003) 1–113 MR1998478
30 L Hesselholt, I Madsen, On the De Rham–Witt complex in mixed characteristic, Ann. Sci. École Norm. Sup. (4) 37 (2004) 1–43 MR2050204
31 G Hochschild, B Kostant, A Rosenberg, Differential forms on regular affine algebras, Trans. Amer. Math. Soc. 102 (1962) 383–408 MR0142598
32 M Hovey, B Shipley, J Smith, Symmetric spectra, J. Amer. Math. Soc. 13 (2000) 149–208 MR1695653
33 L Illusie, Complexe de de\thinspace Rham–Witt et cohomologie cristalline, Ann. Sci. École Norm. Sup. (4) 12 (1979) 501–661 MR565469
34 L Illusie, An overview of the work of K Fujiwara, K Kato, and C Nakayama on logarithmic étale cohomology, Cohomologies p–adiques et applications arithmétiques, II, Astérisque (2002) 271–322 MR1922832
35 K Kato, Logarithmic structures of Fontaine–Illusie, from: "Algebraic analysis, geometry, and number theory (Baltimore, MD, 1988)" (editor J I Igusa), Johns Hopkins Univ. Press (1989) 191–224 MR1463703
36 K Kato, C Nakayama, Log Betti cohomology, log étale cohomology, and log de Rham cohomology of log schemes over C, Kodai Math. J. 22 (1999) 161–186 MR1700591
37 S O Kochman, Homology of the classical groups over the Dyer–Lashof algebra, Trans. Amer. Math. Soc. 185 (1973) 83–136 MR0331386
38 A Langer, T Zink, De Rham–Witt cohomology for a proper and smooth morphism, J. Inst. Math. Jussieu 3 (2004) 231–314 MR2055710
39 L G Lewis Jr., J P May, M Steinberger, J E McClure, Equivariant stable homotopy theory, Lecture Notes in Math. 1213, Springer (1986) MR866482 With contributions by J E McClure
40 P Lima-Filho, Completions and fibrations for topological monoids, Trans. Amer. Math. Soc. 340 (1993) 127–147 MR1134758
41 A Lindenstrauss, I Madsen, Topological Hochschild homology of number rings, Trans. Amer. Math. Soc. 352 (2000) 2179–2204 MR1707702
42 J L Loday, Cyclic homology, Grund. der Math. Wissenschaften 301, Springer (1998) MR1600246 Appendix E by M O Ronco, Chapter 13 by the author in collaboration with T Pirashvili
43 S Lunøe-Nielsen, J Rognes, On the Tate construction of topological Hoch­schild homology and its relation to the construction of Singer, in preparation
44 S Mac Lane, Categories for the working mathematician, Graduate Texts in Math. 5, Springer (1998) MR1712872
45 J P May, The geometry of iterated loop spaces, Lectures Notes in Math. 271, Springer (1972) MR0420610
46 J P May, E ring spaces and E ring spectra, Lecture Notes in Math. 577, Springer (1977) 268 MR0494077 With contributions by F Quinn, N Ray, and J Tornehave
47 J P May, What precisely are E ring spaces and E ring spectra?, from: "New topological contexts for Galois theory and algebraic geometry (BIRS 2008)" (editors A Baker, B Richter), Geom. Topol. Monogr. 16 (2009) 215–282
48 R McCarthy, V Minasian, HKR theorem for smooth S–algebras, J. Pure Appl. Algebra 185 (2003) 239–258 MR2006429
49 J E McClure, R E Staffeldt, On the topological Hochschild homology of bu. I, Amer. J. Math. 115 (1993) 1–45 MR1209233
50 J S Milne, Arithmetic duality theorems, Perspectives in Math. 1, Academic Press (1986) MR881804
51 V Minasian, André–Quillen spectral sequence for THH, Topology Appl. 129 (2003) 273–280 MR1962984
52 C Nakayama, Logarithmic étale cohomology, Math. Ann. 308 (1997) 365–404 MR1457738
53 W Nizioł, K–theory of log-schemes. I, Doc. Math. 13 (2008) 505–551 MR2452875
54 M C Olsson, Logarithmic geometry and algebraic stacks, Ann. Sci. École Norm. Sup. (4) 36 (2003) 747–791 MR2032986
55 M C Olsson, The logarithmic cotangent complex, Math. Ann. 333 (2005) 859–931 MR2195148
56 T Pirashvili, Hodge decomposition for higher order Hochschild homology, Ann. Sci. École Norm. Sup. (4) 33 (2000) 151–179 MR1755114
57 T Pirashvili, B Richter, Robinson–Whitehouse complex and stable homotopy, Topology 39 (2000) 525–530 MR1746906
58 D Puppe, Homotopie und Homologie in abelschen Gruppen- und Monoidkomplexen. I. II, Math. Z. 68 (1958) 367–406, 407–421 MR0093761
59 D G Quillen, Homotopical algebra, Lecture Notes in Math. 43, Springer (1967) MR0223432
60 D Quillen, On the (co-) homology of commutative rings, from: "Applications of Categorical Algebra (Proc. Sympos. Pure Math., Vol. XVII, New York, 1968)", Amer. Math. Soc. (1970) 65–87 MR0257068
61 D Quillen, Higher algebraic K–theory. I, from: "Algebraic K–theory, I: Higher K-theories (Proc. Conf., Battelle Memorial Inst., Seattle, Wash., 1972)" (editor H Bass), Lecture Notes in Math. 341, Springer (1973) 85–147 MR0338129
62 D Quillen, Higher algebraic K–theory, from: "Proceedings of the International Congress of Mathematicians (Vancouver, B. C., 1974), Vol. 1", Canad. Math. Congress (1975) 171–176 MR0422392
63 A Robinson, S Whitehouse, Operads and Γ–homology of commutative rings, Math. Proc. Cambridge Philos. Soc. 132 (2002) 197–234 MR1874215
64 J Rognes, Two-primary algebraic K–theory of pointed spaces, Topology 41 (2002) 873–926 MR1923990
65 J Rognes, The smooth Whitehead spectrum of a point at odd regular primes, Geom. Topol. 7 (2003) 155–184 MR1988283
66 J Rognes, C Weibel, Two-primary algebraic K–theory of rings of integers in number fields, J. Amer. Math. Soc. 13 (2000) 1–54 MR1697095 Appendix A by M Kolster
67 S Sagave, C Schlichtkrull, Diagram spaces and symmetric spectra, in preparation
68 C Schlichtkrull, Units of ring spectra and their traces in algebraic K–theory, Geom. Topol. 8 (2004) 645–673 MR2057776
69 C Schlichtkrull, The homotopy infinite symmetric product represents stable homotopy, Algebr. Geom. Topol. 7 (2007) 1963–1977 MR2366183
70 C Schlichtkrull, Thom spectra that are symmetric spectra arXiv:0811.0592
71 C Schlichtkrull, Group completion in I–spaces, in preparation
72 S Schwede, Spectra in model categories and applications to the algebraic cotangent complex, J. Pure Appl. Algebra 120 (1997) 77–104 MR1466099
73 S Schwede, An untitled book project about symmetric spectra, Manuscript (2007)
74 G Segal, Configuration-spaces and iterated loop-spaces, Invent. Math. 21 (1973) 213–221 MR0331377
75 J P Serre, Local fields, Graduate Texts in Math. 67, Springer (1979) MR554237 Translated from the French by M J Greenberg
76 V P Snaith, A stable decomposition of Ω nSnX, J. London Math. Soc. (2) 7 (1974) 577–583 MR0339155
77 N P Strickland, Realising formal groups, Algebr. Geom. Topol. 3 (2003) 187–205 MR1997319
78 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, Y Manin, K A Ribet), Progr. Math. 88, Birkhäuser (1990) 247–435 MR1106918
79 F Waldhausen, Algebraic K–theory of topological spaces. II, from: "Algebraic topology, Aarhus 1978 (Proc. Sympos., Univ. Aarhus, 1978)" (editors J L Dupont, I Madsen), Lecture Notes in Math. 763, Springer (1979) 356–394 MR561230
80 F Waldhausen, Algebraic K–theory of spaces, from: "Algebraic and geometric topology (New Brunswick, N.J., 1983)" (editors A Ranicki, N Levitt, F Quinn), Lecture Notes in Math. 1126, Springer (1985) 318–419 MR802796
81 F Waldhausen, B Jahren, J Rognes, Spaces of PL manifolds and categories of simple maps, Preprint
82 A Yamaguchi, Morava K–theory of double loop spaces of spheres, Math. Z. 199 (1988) 511–523 MR968317