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Homotopy completion and topological Quillen homology of structured ring spectra

John E Harper and Kathryn Hess

Geometry & Topology 17 (2013) 1325–1416
Bibliography
1 M André, Homologie des algèbres commutatives, 206, Springer (1974) MR0352220
2 G Arone, M Ching, Operads and chain rules for the calculus of functors, Astérisque 338, Soc. Math. France (2011) 158 MR2840569
3 G Arone, M Kankaanrinta, A functorial model for iterated Snaith splitting with applications to calculus of functors, from: "Stable and unstable homotopy" (editors W G Dwyer, S Halperin, R Kane, S O Kochman, M E Mahowald, P S Selick), Fields Inst. Commun. 19, Amer. Math. Soc. (1998) 1 MR1622334
4 A Baker, H Gilmour, P Reinhard, Topological André–Quillen homology for cellular commutative S–algebras, Abh. Math. Semin. Univ. Hambg. 78 (2008) 27 MR2501527
5 A Baker, B Richter, editors, Structured ring spectra, 315, Cambridge University Press (2004) MR2122150
6 M Basterra, André–Quillen cohomology of commutative S–algebras, J. Pure Appl. Algebra 144 (1999) 111 MR1732625
7 M Basterra, M A Mandell, Homology and cohomology of E ring spectra, Math. Z. 249 (2005) 903 MR2126222
8 M Basterra, M A Mandell, Homology of En ring spectra and iterated THH, Algebr. Geom. Topol. 11 (2011) 939 MR2782549
9 A K Bousfield, D M Kan, Homotopy limits, completions and localizations, 304, Springer (1972) MR0365573
10 G Carlsson, Equivariant stable homotopy and Sullivan’s conjecture, Invent. Math. 103 (1991) 497 MR1091616
11 G Carlsson, Derived completions in stable homotopy theory, J. Pure Appl. Algebra 212 (2008) 550 MR2365333
12 D Chataur, J L Rodríguez, J Scherer, Realizing operadic plus-constructions as nullifications, K–Theory 33 (2004) 1 MR2199787
13 M Ching, Bar-cobar duality for operads in stable homotopy theory, J. Topol. 5 (2012) 39 MR2897049
14 D Dugger, D C Isaksen, Topological hypercovers and 𝔸1–realizations, Math. Z. 246 (2004) 667 MR2045835
15 W G Dwyer, Strong convergence of the Eilenberg–Moore spectral sequence, Topology 13 (1974) 255 MR0394663
16 W G Dwyer, J P C Greenlees, S Iyengar, Duality in algebra and topology, Adv. Math. 200 (2006) 357 MR2200850
17 W G Dwyer, J Spaliński, Homotopy theories and model categories, from: "Handbook of algebraic topology" (editor I M James), North-Holland (1995) 73 MR1361887
18 A D Elmendorf, I Kriz, M A Mandell, J P May, Rings, modules, and algebras in stable homotopy theory, 47, Amer. Math. Soc. (1997) MR1417719
19 A D Elmendorf, M A Mandell, Rings, modules, and algebras in infinite loop space theory, Adv. Math. 205 (2006) 163 MR2254311
20 B Fresse, Lie theory of formal groups over an operad, J. Algebra 202 (1998) 455 MR1617616
21 B Fresse, Koszul duality of operads and homology of partition posets, from: "Homotopy theory : relations with algebraic geometry, group cohomology, and algebraic K–theory" (editors P Goerss, S Priddy), Contemp. Math. 346, Amer. Math. Soc. (2004) 115 MR2066499
22 B Fresse, Modules over operads and functors, 1967, Springer (2009) MR2494775
23 V Ginzburg, M Kapranov, Koszul duality for operads, Duke Math. J. 76 (1994) 203 MR1301191
24 P G Goerss, On the André–Quillen cohomology of commutative F2–algebras, Astérisque 186, Soc. Math. France (1990) 169 MR1089001
25 P G Goerss, M J Hopkins, André–Quillen (co)-homology for simplicial algebras over simplicial operads, from: "Une dégustation topologique : Homotopy theory in the Swiss Alps" (editors D Arlettaz, K Hess), Contemp. Math. 265, Amer. Math. Soc. (2000) 41 MR1803952
26 P G Goerss, M J Hopkins, Moduli spaces of commutative ring spectra, from: "Structured ring spectra" (editors A Baker, B Richter), London Math. Soc. Lecture Note Ser. 315, Cambridge Univ. Press (2004) 151 MR2125040
27 P G Goerss, J F Jardine, Simplicial homotopy theory, 174, Birkhäuser (1999) MR1711612
28 P Goerss, K Schemmerhorn, Model categories and simplicial methods, from: "Interactions between homotopy theory and algebra" (editors L L Avramov, J D Christensen, W G Dwyer, M A Mandell, B E Shipley), Contemp. Math. 436, Amer. Math. Soc. (2007) 3 MR2355769
29 T G Goodwillie, Calculus, II : Analytic functors, K–Theory 5 (1991/92) 295 MR1162445
30 T G Goodwillie, Calculus, III : Taylor series, Geom. Topol. 7 (2003) 645 MR2026544
31 J E Harper, Homotopy theory of modules over operads in symmetric spectra, Algebr. Geom. Topol. 9 (2009) 1637 MR2539191
32 J E Harper, Bar constructions and Quillen homology of modules over operads, Algebr. Geom. Topol. 10 (2010) 87 MR2580430
33 J E Harper, Homotopy theory of modules over operads and non-Σ operads in monoidal model categories, J. Pure Appl. Algebra 214 (2010) 1407 MR2593672
34 K Hess, A general framework for homotopic descent and codescent (2010) arXiv:1001.1556v3
35 V Hinich, Homological algebra of homotopy algebras, Comm. Algebra 25 (1997) 3291 MR1465117
36 P S Hirschhorn, Model categories and their localizations, 99, Amer. Math. Soc. (2003) MR1944041
37 J Hornbostel, Preorientations of the derived motivic multiplicative group (2011) arXiv:1005.4546v2
38 M Hovey, Model categories, 63, Amer. Math. Soc. (1999) MR1650134
39 M Hovey, B Shipley, J Smith, Symmetric spectra, J. Amer. Math. Soc. 13 (2000) 149 MR1695653
40 J F Jardine, Generalized étale cohomology theories, 146, Birkhäuser (1997) MR1437604
41 B Johnson, R McCarthy, Deriving calculus with cotriples, Trans. Amer. Math. Soc. 356 (2004) 757 MR2022719
42 I Kříž, J P May, Operads, algebras, modules and motives, Astérisque 233, Soc. Math. France (1995) MR1361938
43 N J Kuhn, Localization of André–Quillen–Goodwillie towers, and the periodic homology of infinite loopspaces, Adv. Math. 201 (2006) 318 MR2211532
44 N J Kuhn, Goodwillie towers and chromatic homotopy : An overview, from: "Proceedings of the Nishida Fest" (editors M Ando, N Minami, J Morava, W S Wilson), Geom. Topol. Monogr. 10 (2007) 245 MR2402789
45 T Lawson, The plus-construction, Bousfield localization, and derived completion, J. Pure Appl. Algebra 214 (2010) 596 MR2577665
46 A Lazarev, Cohomology theories for highly structured ring spectra, from: "Structured ring spectra" (editors A Baker, B Richter), London Math. Soc. Lecture Note Ser. 315, Cambridge Univ. Press (2004) 201 MR2125041
47 M Livernet, Homotopie rationnelle des algèbres sur une opérade, PhD thesis, Université Louis Pasteur (1998) MR1695322
48 M Livernet, On a plus-construction for algebras over an operad, K–Theory 18 (1999) 317 MR1738897
49 S Mac Lane, Homology, 114, Academic (1963) MR0156879
50 S Mac Lane, Categories for the working mathematician, 5, Springer (1998) MR1712872
51 M A Mandell, E algebras and p–adic homotopy theory, Topology 40 (2001) 43 MR1791268
52 M A Mandell, Topological André–Quillen cohomology and E André–Quillen cohomology, Adv. Math. 177 (2003) 227 MR1990939
53 M A Mandell, J P May, S Schwede, B Shipley, Model categories of diagram spectra, Proc. London Math. Soc. (3) 82 (2001) 441 MR1806878
54 R McCarthy, V Minasian, On triples, operads, and generalized homogeneous functors arXiv:math/0401346v1
55 J McClure, R Schwänzl, R Vogt, THH(R)R S1 for E ring spectra, J. Pure Appl. Algebra 121 (1997) 137 MR1473888
56 J E McClure, J H Smith, A solution of Deligne’s Hochschild cohomology conjecture, from: "Recent progress in homotopy theory" (editors D M Davis, J Morava, G Nishida, W S Wilson, N Yagita), Contemp. Math. 293, Amer. Math. Soc. (2002) 153 MR1890736
57 H Miller, The Sullivan conjecture on maps from classifying spaces, Ann. of Math. (2) 120 (1984) 39 MR750716
58 V Minasian, André–Quillen spectral sequence for THH, Topology Appl. 129 (2003) 273 MR1962984
59 D G Quillen, Homotopical algebra, 43, Springer (1967) MR0223432
60 D Quillen, On the (co-) homology of commutative rings, from: "Applications of Categorical Algebra" (editor A Heller), Proc. Sympos. Pure Math. 17, Amer. Math. Soc. (1970) 65 MR0257068
61 C W Rezk, Spaces of algebra structures and cohomology of operads, PhD thesis, Massachusetts Institute of Technology (1996) MR2716655
62 B Richter, An Atiyah–Hirzebruch spectral sequence for topological André–Quillen homology, J. Pure Appl. Algebra 171 (2002) 59 MR1903396
63 J Rognes, Galois extensions of structured ring spectra : Stably dualizable groups, 192, Amer. Math. Soc. (2008) MR2387923
64 J Rognes, Topological logarithmic structures, from: "New topological contexts for Galois theory and algebraic geometry" (editors A Baker, B Richter), Geom. Topol. Monogr. 16 (2009) 401 MR2544395
65 S Schwede, Spectra in model categories and applications to the algebraic cotangent complex, J. Pure Appl. Algebra 120 (1997) 77 MR1466099
66 S Schwede, S–modules and symmetric spectra, Math. Ann. 319 (2001) 517 MR1819881
67 S Schwede, Stable homotopy of algebraic theories, Topology 40 (2001) 1 MR1791267
68 S Schwede, An untitled book project about symmetric spectra, preprint (2007)
69 S Schwede, On the homotopy groups of symmetric spectra, Geom. Topol. 12 (2008) 1313 MR2421129
70 S Schwede, B E Shipley, Algebras and modules in monoidal model categories, Proc. London Math. Soc. (3) 80 (2000) 491 MR1734325
71 B Shipley, A convenient model category for commutative ring spectra, from: "Homotopy theory : Relations with algebraic geometry, group cohomology, and algebraic K–theory" (editors P Goerss, S Priddy), Contemp. Math. 346, Amer. Math. Soc. (2004) 473 MR2066511
72 D Sullivan, Geometric topology, I : Localization, periodicity, and Galois symmetry, Massachusetts Institute of Technology (1971) MR0494074
73 D Sullivan, Genetics of homotopy theory and the Adams conjecture, Ann. of Math. (2) 100 (1974) 1 MR0442930
74 J M Turner, On simplicial commutative algebras with vanishing André–Quillen homology, Invent. Math. 142 (2000) 547 MR1804160
75 C A Weibel, An introduction to homological algebra, 38, Cambridge University Press (1994) MR1269324