Algebraic & Geometric Topology Volume 16, issue 4 (2016)

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Localizations of abelian Eilenberg–Mac Lane spaces of finite type

Carles Casacuberta, José L Rodríguez and Jin-yen Tai

Algebraic & Geometric Topology 16 (2016) 2379–2420

DOI: 10.2140/agt.2016.16.2379

Bibliography

1	J Adámek, J Rosický, Locally presentable and accessible categories, 189, Cambridge Univ. Press (1994) MR1294136
2	B Badzioch, Recognition principle for generalized Eilenberg–Mac Lane spaces, from: "Cohomological methods in homotopy theory" (editors J Aguadé, C Broto, C Casacuberta), Progr. Math. 196, Birkhäuser (2001) 21 MR1851244
3	B Badzioch, M Feshbach, A note on localizations of perfect groups, Proc. Amer. Math. Soc. 133 (2005) 693 MR2113917
4	M Blomgren, W Chachólski, E D Farjoun, Y Segev, Idempotent transformations of finite groups, Adv. Math. 233 (2013) 56 MR2995665
5	A K Bousfield, Types of acyclicity, J. Pure Appl. Algebra 4 (1974) 293 MR0367978
6	A K Bousfield, Constructions of factorization systems in categories, J. Pure Appl. Algebra 9 (1976/77) 207 MR0478159
7	A K Bousfield, On homology equivalences and homological localizations of spaces, Amer. J. Math. 104 (1982) 1025 MR675308
8	A K Bousfield, Localization and periodicity in unstable homotopy theory, J. Amer. Math. Soc. 7 (1994) 831 MR1257059
9	A K Bousfield, Unstable localization and periodicity, from: "Algebraic topology: new trends in localization and periodicity" (editors C Broto, C Casacuberta, G Mislin), Progr. Math. 136, Birkhäuser (1996) 33 MR1397720
10	A K Bousfield, Homotopical localizations of spaces, Amer. J. Math. 119 (1997) 1321 MR1481817
11	A K Bousfield, D M Kan, The core of a ring, J. Pure Appl. Algebra 2 (1972) 73 MR0308107
12	R A Bowshell, P Schultz, Unital rings whose additive endomorphisms commute, Math. Ann. 228 (1977) 197 MR0498691
13	G Braun, R Göbel, E–algebras whose torsion part is not cyclic, Proc. Amer. Math. Soc. 133 (2005) 2251 MR2138867
14	K S Brown, Cohomology of groups, 87, Springer (1982) MR672956
15	J Buckner, M Dugas, Co-local subgroups of abelian groups, from: "Abelian groups, rings, modules, and homological algebra" (editors P Goeters, O M G Jenda), Lect. Notes Pure Appl. Math. 249, Chapman & Hall/CRC (2006) 29 MR2229098
16	J Buckner, M Dugas, Co-local subgroups of nilpotent groups of class 2, from: "Models, modules and abelian groups" (editors R Göbel, B Goldsmith), Walter de Gruyter (2008) 351 MR2513250
17	C Casacuberta, Recent advances in unstable localization, from: "The Hilton Symposium 1993" (editor G Mislin), CRM Proc. Lecture Notes 6, Amer. Math. Soc. (1994) 1 MR1290581
18	C Casacuberta, Anderson localization from a modern point of view, from: "The Čech centennial" (editors M Cenkl, H Miller), Contemp. Math. 181, Amer. Math. Soc. (1995) 35 MR1320986
19	C Casacuberta, On structures preserved by idempotent transformations of groups and homotopy types, from: "Crystallographic groups and their generalizations" (editors P Igodt, H Abels, Y Félix, F Grunewald), Contemp. Math. 262, Amer. Math. Soc. (2000) 39 MR1796125
20	C Casacuberta, J J Gutiérrez, Homotopical localizations of module spectra, Trans. Amer. Math. Soc. 357 (2005) 2753 MR2139526
21	C Casacuberta, J J Gutiérrez, I Moerdijk, R M Vogt, Localization of algebras over coloured operads, Proc. Lond. Math. Soc. 101 (2010) 105 MR2661243
22	C Casacuberta, O Raventós, A Tonks, Comparing localizations across adjunctions, preprint (2014) arXiv:1404.7340
23	C Casacuberta, J L Rodríguez, On towers approximating homological localizations, J. London Math. Soc. 56 (1997) 645 MR1610420
24	W Chachólski, E Damian, E D Farjoun, Y Segev, The A–core and A–cover of a group, J. Algebra 321 (2009) 631 MR2483285
25	W Dicks, W Stephenson, Epimorphs and dominions of Dedekind domains, J. London Math. Soc. 29 (1984) 224 MR744090
26	A Dold, R Thom, Quasifaserungen und unendliche symmetrische Produkte, Ann. of Math. 67 (1958) 239 MR0097062
27	M Dugas, Localizations of torsion-free abelian groups, J. Algebra 278 (2004) 411 MR2068086
28	M Dugas, Localizations of torsion-free abelian groups, II, J. Algebra 284 (2005) 811 MR2114581
29	M Dugas, Co-local subgroups of abelian groups, II, J. Pure Appl. Algebra 208 (2007) 117 MR2269833
30	M Dugas, A Mader, C Vinsonhaler, Large E–rings exist, J. Algebra 108 (1987) 88 MR887193
31	W G Dwyer, J H Palmieri, Ohkawa’s theorem : there is a set of Bousfield classes, Proc. Amer. Math. Soc. 129 (2001) 881 MR1712921
32	E D Farjoun, Cellular spaces, null spaces and homotopy localization, 1622, Springer (1996) MR1392221
33	E D Farjoun, R Göbel, Y Segev, Cellular covers of groups, J. Pure Appl. Algebra 208 (2007) 61 MR2269828
34	E D Farjoun, R Göbel, Y Segev, S Shelah, On kernels of cellular covers, Groups Geom. Dyn. 1 (2007) 409 MR2357479
35	L Fuchs, R Göbel, Cellular covers of abelian groups, Results Math. 53 (2009) 59 MR2481406
36	R Göbel, B Goldsmith, Classifying E-algebras over Dedekind domains, J. Algebra 306 (2006) 566 MR2271354
37	R Göbel, J L Rodríguez, S Shelah, Large localizations of finite simple groups, J. Reine Angew. Math. 550 (2002) 1 MR1925906
38	R Göbel, J L Rodríguez, L Strüngmann, Cellular covers of cotorsion-free modules, Fund. Math. 217 (2012) 211 MR2943679
39	R Göbel, S Shelah, Constructing simple groups for localizations, Comm. Algebra 30 (2002) 809 MR1883027
40	R Göbel, L Strüngmann, Almost-free E(R)–algebras and E(A,R)–modules, Fund. Math. 169 (2001) 175 MR1852380
41	R Göbel, J Trlifaj, Approximations and endomorphism algebras of modules, 41, Walter de Gruyter (2006) MR2251271
42	R Göbel, J Trlifaj, Approximations and endomorphism algebras of modules, 2 : Predictions, 41, Walter de Gruyter (2012) MR2985654
43	J J Gutiérrez, Localización y conservación de estructuras en homotopía estable, PhD thesis, Universitat de Barcelona (2004)
44	J J Gutiérrez, Homological localizations of Eilenberg–MacLane spectra, Forum Math. 22 (2010) 349 MR2607569
45	J J Gutiérrez, Cellularization of structures in stable homotopy categories, Math. Proc. Cambridge Philos. Soc. 153 (2012) 399 MR2990623
46	A Hatcher, Algebraic topology, Cambridge Univ. Press (2002) MR1867354
47	P S Hirschhorn, Model categories and their localizations, 99, Amer. Math. Soc. (2003) MR1944041
48	I Kaplansky, Infinite abelian groups, The University of Michigan Press (1969) MR0233887
49	A Libman, Cardinality and nilpotency of localizations of groups and G–modules, Israel J. Math. 117 (2000) 221 MR1760593
50	S Mac Lane, Categories for the working mathematician, 5, Springer (1971) MR0354798
51	J P May, Simplicial objects in algebraic topology, 11, D Van Nostrand Co (1967) MR0222892
52	J P May, Infinite loop space theory, Bull. Amer. Math. Soc. 83 (1977) 456 MR0451235
53	H Miller, The Sullivan conjecture on maps from classifying spaces, Ann. of Math. 120 (1984) 39 MR750716
54	G Mislin, Localization with respect to K–theory, J. Pure Appl. Algebra 10 (1977/78) 201 MR0467732
55	R J Nunke, Modules of extensions over Dedekind rings, Illinois J. Math. 3 (1959) 222 MR0102538
56	T Ohkawa, The injective hull of homotopy types with respect to generalized homology functors, Hiroshima Math. J. 19 (1989) 631 MR1035147
57	N O’Sullivan, Localizations of free soluble groups, J. Group Theory 4 (2001) 89 MR1808841
58	C Parker, J Saxl, Localization and finite simple groups, Israel J. Math. 153 (2006) 285 MR2254646
59	R S Pierce, E–modules, from: "Abelian group theory" (editors L Fuchs, R Göbel, P Schultz), Contemp. Math. 87, Amer. Math. Soc. (1989) 221 MR995278
60	R S Pierce, C I Vinsonhaler, Classifying E–rings, Comm. Algebra 19 (1991) 615 MR1100367
61	D J S Robinson, A course in the theory of groups, 80, Springer (1996) MR1357169
62	J L Rodríguez, On homotopy colimits of spaces with a single homology or homotopy group, PhD thesis, Universitat Autònoma de Barcelona (1997)
63	J L Rodríguez, J Scherer, Cellular approximations using Moore spaces, from: "Cohomological methods in homotopy theory" (editors J Aguadé, C Broto, C Casacuberta), Progr. Math. 196, Birkhäuser (2001) 357 MR1851263
64	J L Rodríguez, J Scherer, A connection between cellularization for groups and spaces via two-complexes, J. Pure Appl. Algebra 212 (2008) 1664 MR2400735
65	J L Rodríguez, J Scherer, L Strüngmann, On localization of torsion abelian groups, Fund. Math. 183 (2004) 123 MR2127962
66	J L Rodríguez, J Scherer, J Thévenaz, Finite simple groups and localization, Israel J. Math. 131 (2002) 185 MR1942308
67	J L Rodríguez, J Scherer, A Viruel, Preservation of perfectness and acyclicity : Berrick and Casacuberta’s universal acyclic space localized at a set of primes, Forum Math. 17 (2005) 67 MR2110538
68	J L Rodríguez, J Scherer, A Viruel, Non-simple localizations of finite simple groups, J. Algebra 305 (2006) 765 MR2266851
69	J L Rodríguez, L Strüngmann, On cellular covers with free kernels, Mediterr. J. Math. 9 (2012) 295 MR2917105
70	P Schultz, The endomorphism ring of the additive group of a ring, J. Austral. Math. Soc. 15 (1973) 60 MR0338218
71	B Stenström, Rings of quotients, 217, Springer (1975) MR0389953
72	L Strüngmann, Almost-free E(R)–algebras over countable domains, PhD thesis, Universität Essen (1998)
73	J y Tai, On f–localization functors and connectivity, 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) 285 MR1622354
74	J y Tai, A version of Zabrodsky’s lemma, Proc. Amer. Math. Soc. 126 (1998) 1573 MR1443169
75	G W Whitehead, Elements of homotopy theory, 61, Springer (1978) MR516508
76	G V Wilson, Additive groups of T–rings, Proc. Amer. Math. Soc. 99 (1987) 219 MR870774