Volume 15, issue 4 (2015)

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Completed power operations for Morava $E$–theory

Tobias Barthel and Martin Frankland

Algebraic & Geometric Topology 15 (2015) 2065–2131
Bibliography
1 J Adámek, J Rosický, E M Vitale, What are sifted colimits?, Theory Appl. Categ. 23 (2010) 251 MR2720191
2 J Adámek, J Rosický, E M Vitale, Algebraic theories, Cambridge Tracts in Math. 184, Cambridge Univ. Press (2011) MR2757312
3 M Ando, Notes on formal groups, unpublished notes based on a course taught by Michael Hopkins at MIT in the spring of 1990
4 M Ando, Isogenies of formal group laws and power operations in the cohomology theories $E_n$, Duke Math. J. 79 (1995) 423 MR1344767
5 A Baker, $L$–complete Hopf algebroids and their comodules, from: "Alpine perspectives on algebraic topology" (editors C Ausoni, K Hess, J Scherer), Contemp. Math. 504, Amer. Math. Soc. (2009) 1 MR2581903
6 M Behrens, C Rezk, The Bousfield–Kuhn functor and topological André–Quillen cohomology (2012)
7 J Borger, B Wieland, Plethystic algebra, Advances Math. 194 (2005) 246 MR2139914
8 A K Bousfield, On $\lambda$–rings and the $K$–theory of infinite loop spaces, $K$–Theory 10 (1996) 1 MR1373816
9 A K Bousfield, D M Kan, Homotopy limits, completions and localizations, Lecture Notes in Math. 304, Springer (1972) MR0365573
10 R R Bruner, J P May, J E McClure, M Steinberger, $H_\infty $ ring spectra and their applications, Lecture Notes in Math. 1176, Springer (1986) MR836132
11 M Demazure, Lectures on $p$–divisible groups, Lecture Notes in Mathematics 302, Springer (1986) MR883960
12 A D Elmendorf, I Kriz, M A Mandell, J P May, Rings, modules and algebras in stable homotopy theory, Math. Surveys and Monographs 47, Amer. Math. Soc. (1997) MR1417719
13 P G Goerss, H W Henn, M Mahowald, C Rezk, A resolution of the $K(2)$–local sphere at the prime $3$, Ann. of Math. 162 (2005) 777 MR2183282
14 P G Goerss, M J Hopkins, André–Quillen (co)homology for simplicial algebras over simplicial operads, from: "Une dégustation topologique (Topological morsels): Homotopy theory in the Swiss Alps" (editors D Arlettaz, K Hess), Contemp. Math. 265, Amer. Math. Soc. (2000) 41 MR1803952
15 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
16 J P C Greenlees, J P May, Derived functors of $I$–adic completion and local homology, J. Algebra 149 (1992) 438 MR1172439
17 M J Hopkins, $K(1)$–local $E_\infty$–ring spectra, from: "Topological modular forms", Math. Surveys Monogr. 201, Amer. Math. Soc. (2014) 287 MR3328537
18 M J Hopkins, M Mahowald, H Sadofsky, Constructions of elements in Picard groups, from: "Topology and representation theory" (editors E M Friedlander, M E Mahowald), Contemp. Math. 158, Amer. Math. Soc. (1994) 89 MR1263713
19 M J Hopkins, J H Smith, Nilpotence and stable homotopy theory, II, Ann. of Math. 148 (1998) 1 MR1652975
20 M Hovey, Some spectral sequences in Morava $E$–theory (2004)
21 M Hovey, Morava $E$–theory of filtered colimits, Trans. Amer. Math. Soc. 360 (2008) 369 MR2342007
22 M Hovey, N P Strickland, Morava $K$–theories and localisation, Mem. Amer. Math. Soc. 139, Amer. Math. Soc. (1999) MR1601906
23 A Joyal, Quasi-categories and Kan complexes, J. Pure Appl. Algebra 175 (2002) 207 MR1935979
24 G Laures, An $E_\infty$ splitting of spin bordism, Amer. J. Math. 125 (2003) 977 MR2004426
25 J Lurie, Higher topos theory, Annals of Math. Studies 170, Princeton Univ. Press (2009) MR2522659
26 J Lurie, Higher algebra (2014)
27 S Mac Lane, Categories for the working mathematician, Graduate Texts in Math. 5, Springer (1998) MR1712872
28 C Rezk, Power operations for Morava $E$–theory of height $2$ at the prime $2$, arXiv:0812.1320
29 C Rezk, Rings of power operations for Morava $E$–theories are Koszul, arXiv:1204.4831
30 C Rezk, The congruence criterion for power operations in Morava $E$–theory, Homology, Homotopy Appl. 11 (2009) 327 MR2591924
31 C Rezk, Analytic completion (2013)
32 C Rezk, Power operations in Morava $E$–theory: Structure and calculations (2013)
33 B Richter, An Atiyah–Hirzebruch spectral sequence for topological André–Quillen homology, J. Pure Appl. Algebra 171 (2002) 59 MR1903396
34 E Riehl, Categorical homotopy theory, New Math. Monographs 24, Cambridge Univ. Press (2014) MR3221774
35 A Salch, Approximation of subcategories by abelian subcategories, (2010) arXiv:1006.0048
36 , Stacks project (2014)
37 N P Strickland, Morava $E$–theory of symmetric groups, Topology 37 (1998) 757 MR1607736
38 N P Strickland, Gross–Hopkins duality, Topology 39 (2000) 1021 MR1763961
39 G Valenzuela, Homological algebra of complete and torsion modules, PhD thesis, Wesleyan University (2015)
40 D Yau, Lambda-rings, World Scientific (2010) MR2649360
41 A Yekutieli, On flatness and completion for infinitely generated modules over Noetherian rings, Comm. Algebra 39 (2011) 4221 MR2855123
42 Y Zhu, The power operation structure on Morava $E$–theory of height $2$ at the prime $3$, Algebr. Geom. Topol. 14 (2014) 953 MR3160608