Algebraic & Geometric Topology Volume 21, issue 4 (2021)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

Realising $\pi_\ast^eR$–algebras by global ring spectra

Jack Morgan Davies

Algebraic & Geometric Topology 21 (2021) 1745–1790

DOI: 10.2140/agt.2021.21.1745

Bibliography

1	J F Adams, Stable homotopy and generalised homology, Univ. Chicago Press (1974) MR0402720
2	V Angeltveit, Topological Hochschild homology and cohomology of A_∞ ring spectra, Geom. Topol. 12 (2008) 987 MR2403804
3	A Baker, B Richter, Realizability of algebraic Galois extensions by strictly commutative ring spectra, Trans. Amer. Math. Soc. 359 (2007) 827 MR2255198
4	M Basterra, B Richter, (Co)-homology theories for commutative (S−)algebras, from: "Structured ring spectra" (editors A Baker, B Richter), Lond. Math. Soc. Lect. Note Ser. 315, Cambridge Univ. Press (2004) 115 MR2122156
5	P Belmans, A J de Jong, others, The Stacks project, electronic reference (2005–)
6	C Berger, I Moerdijk, Axiomatic homotopy theory for operads, Comment. Math. Helv. 78 (2003) 805 MR2016697
7	C Berger, I Moerdijk, On the derived category of an algebra over an operad, Georgian Math. J. 16 (2009) 13 MR2527612
8	A J Blumberg, M A Hill, Operadic multiplications in equivariant spectra, norms, and transfers, Adv. Math. 285 (2015) 658 MR3406512
9	A M Bohmann, Global orthogonal spectra, Homology Homotopy Appl. 16 (2014) 313 MR3217308
10	A K Bousfield, D M Kan, Homotopy limits, completions and localizations, 304, Springer (1972) MR0365573
11	R R Bruner, J P May, J E McClure, M Steinberger, H_∞ ring spectra and their applications, 1176, Springer (1986) MR836132
12	J M Davies, Realising algebra in global homotopy in good case, master’s thesis, Universität Bonn (2018)
13	J M Davies, Multiplicative localisations in global homotopy theory, work in progress (2019)
14	W G Dwyer, D M Kan, A classification theorem for diagrams of simplicial sets, Topology 23 (1984) 139 MR744846
15	W G Dwyer, J Spaliński, Homotopy theories and model categories, from: "Handbook of algebraic topology" (editor I M James), North-Holland (1995) 73 MR1361887
16	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
17	P G Goerss, M J Hopkins, Moduli spaces of commutative ring spectra, from: "Structured ring spectra" (editors A Baker, B Richter), Lond. Math. Soc. Lect. Note Ser. 315, Cambridge Univ. Press (2004) 151 MR2125040
18	J P C Greenlees, J P May, Localization and completion theorems for MU–module spectra, Ann. of Math. 146 (1997) 509 MR1491447
19	M Hausmann, Global group laws and equivariant bordism rings, preprint (2019) arXiv:1912.07583
20	M A Hill, M J Hopkins, Equivariant multiplicative closure, from: "Algebraic topology: applications and new directions" (editors U Tillmann, S Galatius, D Sinha), Contemp. Math. 620, Amer. Math. Soc. (2014) 183 MR3290092
21	L G Lewis Jr., J P May, M Steinberger, Equivariant stable homotopy theory, 1213, Springer (1986) MR866482
22	J Lurie, Chromatic homotopy theory, lecture notes (2010)
23	J Lurie, Higher algebra, preprint (2017)
24	M A Mandell, J P May, Equivariant orthogonal spectra and S–modules, 755, Amer. Math. Soc. (2002) MR1922205
25	M A Mandell, J P May, S Schwede, B Shipley, Model categories of diagram spectra, Proc. Lond. Math. Soc. 82 (2001) 441 MR1806878
26	A Neeman, Triangulated categories, 148, Princeton Univ. Press (2001) MR1812507
27	J Noel, H_∞≠E_∞, from: "An alpine expedition through algebraic topology" (editors C Ausoni, K Hess, B Johnson, W Lück, J Scherer), Contemp. Math. 617, Amer. Math. Soc. (2014) 237 MR3243401
28	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
29	A Robinson, Classical obstructions and S–algebras, from: "Structured ring spectra" (editors A Baker, B Richter), Lond. Math. Soc. Lect. Note Ser. 315, Cambridge Univ. Press (2004) 133 MR2122157
30	A Robinson, S Whitehouse, Operads and Γ–homology of commutative rings, Math. Proc. Cambridge Philos. Soc. 132 (2002) 197 MR1874215
31	S Sagave, Universal Toda brackets of ring spectra, Trans. Amer. Math. Soc. 360 (2008) 2767 MR2373333
32	R Schwänzl, R M Vogt, F Waldhausen, Adjoining roots of unity to E_∞ ring spectra in good cases : a remark, from: "Homotopy invariant algebraic structures" (editors J P Meyer, J Morava, W S Wilson), Contemp. Math. 239, Amer. Math. Soc. (1999) 245 MR1718085
33	S Schwede, Global homotopy theory, 34, Cambridge Univ. Press (2018) MR3838307
34	S Schwede, B E Shipley, Algebras and modules in monoidal model categories, Proc. Lond. Math. Soc. 80 (2000) 491 MR1734325
35	D P Sinha, Computations of complex equivariant bordism rings, Amer. J. Math. 123 (2001) 577 MR1844571
36	M Spitzweck, Operads, algebras and modules in model categories and motives, PhD thesis, Universität Bonn (2001)
37	M Stahlhauer, G_∞–ring spectra, master’s thesis, Universität Bonn (2018)
38	J J Wolbert, Classifying modules over K–theory spectra, J. Pure Appl. Algebra 124 (1998) 289 MR1600317