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Chromatic splitting for the $K(2)$–local sphere at $p=2$

Agnès Beaudry, Paul G Goerss and Hans-Werner Henn

Geometry & Topology 26 (2022) 377–476
DOI: 10.2140/gt.2022.26.377
Bibliography
1 A Adem, R J Milgram, Cohomology of finite groups, 309, Springer (1994) MR1317096
2 T Barthel, A Beaudry, Chromatic structures in stable homotopy theory, from: "Handbook of homotopy theory" (editor H Miller), CRC (2020) 163 MR4197985
3 T Bauer, Computation of the homotopy of the spectrum tmf, from: "Groups, homotopy and configuration spaces" (editors N Iwase, T Kohno, R Levi, D Tamaki, J Wu), Geom. Topol. Monogr. 13, Geom. Topol. (2008) 11 MR2508200
4 A Beaudry, The algebraic duality resolution at p = 2, Algebr. Geom. Topol. 15 (2015) 3653 MR3450774
5 A Beaudry, The chromatic splitting conjecture at n = p = 2, Geom. Topol. 21 (2017) 3213 MR3692966
6 A Beaudry, Towards the homotopy of the K(2)–local Moore spectrum at p = 2, Adv. Math. 306 (2017) 722 MR3581316
7 M Behrens, The homotopy groups of SE(2) at p 5 revisited, Adv. Math. 230 (2012) 458 MR2914955
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 R Bruner, Algebraic and geometric connecting homomorphisms in the Adams spectral sequence, from: "Geometric applications of homotopy theory, II" (editors M G Barratt, M E Mahowald), Lecture Notes in Math. 658, Springer (1978) 131 MR513570
10 C Bujard, Finite subgroups of extended Morava stabilizer groups, preprint (2012) arXiv:1206.1951
11 E S Devinatz, A Lyndon–Hochschild–Serre spectral sequence for certain homotopy fixed point spectra, Trans. Amer. Math. Soc. 357 (2005) 129 MR2098089
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 C L Douglas, J Francis, A G Henriques, M A Hill, editors, Topological modular forms, 201, Amer. Math. Soc. (2014) MR3223024
14 P G Goerss, H W Henn, M Mahowald, The rational homotopy of the K(2)–local sphere and the chromatic splitting conjecture for the prime 3 and level 2, Doc. Math. 19 (2014) 1271 MR3312144
15 P 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
16 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
17 H W Henn, A mini-course on Morava stabilizer groups and their cohomology, from: "Algebraic topology" (editors N H V Hung, L Schwartz), Lecture Notes in Math. 2194, Springer (2017) 149 MR3790894
18 H W Henn, The centralizer resolution of the K(2)–local sphere at the prime 2, from: "Homotopy theory: tools and applications" (editors D G Davis, H W Henn, J F Jardine, M W Johnson, C Rezk), Contemp. Math. 729, Amer. Math. Soc. (2019) 93 MR3959597
19 H W Henn, N Karamanov, M Mahowald, The homotopy of the K(2)–local Moore spectrum at the prime 3 revisited, Math. Z. 275 (2013) 953 MR3127044
20 M J Hopkins, B H Gross, The rigid analytic period mapping, Lubin–Tate space, and stable homotopy theory, Bull. Amer. Math. Soc. 30 (1994) 76 MR1217353
21 M J Hopkins, J H Smith, Nilpotence and stable homotopy theory, II, Ann. of Math. 148 (1998) 1 MR1652975
22 M Hovey, Bousfield localization functors and Hopkins’ chromatic splitting conjecture, from: "The Čech centennial" (editors M Cenkl, H Miller), Contemp. Math. 181, Amer. Math. Soc. (1995) 225 MR1320994
23 M Hovey, Operations and co-operations in Morava E–theory, Homology Homotopy Appl. 6 (2004) 201 MR2076002
24 M Hovey, N P Strickland, Morava K–theories and localisation, 666, Amer. Math. Soc. (1999) MR1601906
25 J Kohlhaase, On the Iwasawa theory of the Lubin–Tate moduli space, Compos. Math. 149 (2013) 793 MR3069363
26 O Lader, Une résolution projective pour le second groupe de Morava pour p 5 et applications, PhD thesis, Université de Strasbourg (2013)
27 M Lazard, Groupes analytiques p–adiques, Inst. Hautes Études Sci. Publ. Math. 26 (1965) 389 MR209286
28 W H Lin, D M Davis, M E Mahowald, J F Adams, Calculation of Lin’s Ext groups, Math. Proc. Cambridge Philos. Soc. 87 (1980) 459 MR569195
29 M Mahowald, The image of J in the EHP sequence, Ann. of Math. 116 (1982) 65 MR662118
30 M Mahowald, C Rezk, Topological modular forms of level 3, Pure Appl. Math. Q. 5 (2009) 853 MR2508904
31 H R Miller, D C Ravenel, W S Wilson, Periodic phenomena in the Adams–Novikov spectral sequence, Ann. of Math. 106 (1977) 469 MR458423
32 J Morava, Noetherian localisations of categories of cobordism comodules, Ann. of Math. 121 (1985) 1 MR782555
33 D C Ravenel, The cohomology of the Morava stabilizer algebras, Math. Z. 152 (1977) 287 MR431168
34 D C Ravenel, A novice’s guide to the Adams–Novikov spectral sequence, from: "Geometric applications of homotopy theory, II" (editors M G Barratt, M E Mahowald), Lecture Notes in Math. 658, Springer (1978) 404 MR513586
35 D C Ravenel, Localization with respect to certain periodic homology theories, Amer. J. Math. 106 (1984) 351 MR737778
36 D C Ravenel, Complex cobordism and stable homotopy groups of spheres, 121, Academic (1986) MR860042
37 D C Ravenel, Nilpotence and periodicity in stable homotopy theory, 128, Princeton Univ. Press (1992) MR1192553
38 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
39 K Shimomura, The Adams–Novikov E2–term for computing π(L2V (0)) at the prime 2, Topology Appl. 96 (1999) 133 MR1702307
40 K Shimomura, X Wang, The Adams–Novikov E2–term for π(L2S0) at the prime 2, Math. Z. 241 (2002) 271 MR1935487
41 K Shimomura, A Yabe, The homotopy groups π(L2S0), Topology 34 (1995) 261 MR1318877
42 J H Silverman, The arithmetic of elliptic curves, 106, Springer (1986) MR817210
43 N P Strickland, Gross–Hopkins duality, Topology 39 (2000) 1021 MR1763961
44 N Strickland, Level three structures, preprint (2018) arXiv:1803.09962
45 P Symonds, T Weigel, Cohomology of p–adic analytic groups, from: "New horizons in pro-p groups" (editors M du Sautoy, D Segal, A Shalev), Progr. Math. 184, Birkhäuser (2000) 349 MR1765127