Algebraic & Geometric Topology Volume 20, issue 3 (2020)

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Towards the $K(2)$–local homotopy groups of $Z$

Prasit Bhattacharya and Philip Egger

Algebraic & Geometric Topology 20 (2020) 1235–1277

DOI: 10.2140/agt.2020.20.1235

Bibliography

1	J F Adams, On the groups J(X), IV, Topology 5 (1966) 21 MR198470
2	A Beaudry, The algebraic duality resolution at p = 2, Algebr. Geom. Topol. 15 (2015) 3653 MR3450774
3	A Beaudry, Towards the homotopy of the K(2)–local Moore spectrum at p = 2, Adv. Math. 306 (2017) 722 MR3581316
4	A Beaudry, M Behrens, P Bhattacharya, D Culver, Z Xu, On the tmf–resolution of Z, preprint (2019) arXiv:1909.13379
5	M Behrens, M Hill, M J Hopkins, M Mahowald, On the existence of a v₂³²–self map on M(1,4) at the prime 2, Homology Homotopy Appl. 10 (2008) 45 MR2475617
6	P Bhattacharya, P Egger, A class of 2–local finite spectra which admit a v₂¹–self-map, Adv. Math. 360 (2020) MR4031119
7	P Bhattacharya, P Egger, M Mahowald, On the periodic v₂–self-map of A₁, Algebr. Geom. Topol. 17 (2017) 657 MR3623667
8	I Bobkova, P G Goerss, Topological resolutions in K(2)–local homotopy theory at the prime 2, J. Topol. 11 (2018) 918 MR3989433
9	C Bujard, Finite subgroups of extended Morava stabilizer groups, preprint (2012) arXiv:1206.1951
10	D M Davis, M Mahowald, v₁– and v₂–periodicity in stable homotopy theory, Amer. J. Math. 103 (1981) 615 MR623131
11	E S Devinatz, M J Hopkins, The action of the Morava stabilizer group on the Lubin–Tate moduli space of lifts, Amer. J. Math. 117 (1995) 669 MR1333942
12	E S Devinatz, M J Hopkins, Homotopy fixed point spectra for closed subgroups of the Morava stabilizer groups, Topology 43 (2004) 1 MR2030586
13	M J Hopkins, J H Smith, Nilpotence and stable homotopy theory, II, Ann. of Math. 148 (1998) 1 MR1652975
14	J Lubin, J Tate, Formal moduli for one-parameter formal Lie groups, Bull. Soc. Math. France 94 (1966) 49 MR238854
15	M Mahowald, bo–resolutions, Pacific J. Math. 92 (1981) 365 MR618072
16	M Mahowald, The image of J in the EHP sequence, Ann. of Math. 116 (1982) 65 MR662118
17	H R Miller, On relations between Adams spectral sequences, with an application to the stable homotopy of a Moore space, J. Pure Appl. Algebra 20 (1981) 287 MR604321
18	J Morava, Noetherian localisations of categories of cobordism comodules, Ann. of Math. 121 (1985) 1 MR782555
19	D Quillen, On the formal group laws of unoriented and complex cobordism theory, Bull. Amer. Math. Soc. 75 (1969) 1293 MR253350
20	D C Ravenel, Localization with respect to certain periodic homology theories, Amer. J. Math. 106 (1984) 351 MR737778
21	D C Ravenel, Complex cobordism and stable homotopy groups of spheres, 121, Academic (1986) MR860042
22	D C Ravenel, Nilpotence and periodicity in stable homotopy theory, 128, Princeton Univ. Press (1992) MR1192553
23	C Rezk, Notes on the Hopkins–Miller theorem, from: "Homotopy theory via algebraic geometry and group representations" (editors M Mahowald, S Priddy), Contemp. Math. 220, Amer. Math. Soc. (1998) 313 MR1642902