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On homotopy groups of $E_C^{hG_{24}}\wedge A_1$

Viet-Cuong Pham

Algebraic & Geometric Topology 22 (2022) 3855–3938
Bibliography
1 J F Adams, Stable homotopy and generalised homology, University of Chicago Press (1974) MR0402720
2 D W Anderson, E H Brown Jr., F P Peterson, Pin cobordism and related topics, Comment. Math. Helv. 44 (1969) 462 MR261613
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. Publ. (2008) 11 MR2508200
4 T Bauer, Bousfield localization and the Hasse square, from: "Topological modular forms" (editors C L Douglas, J Francis, A G Henriques, M A Hill), Mathematical Surveys and Monographs 201, Amer. Math. Soc. (2014) 79 MR3223024
5 A Beaudry, The algebraic duality resolution at p = 2, Algebr. Geom. Topol. 15 (2015) 3653 MR3450774
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 M Behrens, The construction of tmf, from: "Topological modular forms" (editors C L Douglas, J Francis, A G Henriques, M A Hill), Mathematical Surveys and Monographs 201, Amer. Math. Soc. (2014) 131 MR3223024
9 M Behrens, K Ormsby, On the homotopy of Q(3) and Q(5) at the prime 2, Algebr. Geom. Topol. 16 (2016) 2459 MR3572338
10 P Bhattacharya, P Egger, M Mahowald, On the periodic v2–self-map of A1, Algebr. Geom. Topol. 17 (2017) 657 MR3623667
11 I Bobkova, P G Goerss, Topological resolutions in K(2)–local homotopy theory at the prime 2, J. Topol. 11 (2018) 918 MR3989433
12 K S Brown, Cohomology of groups, 87, Springer (1982) MR672956
13 D M Davis, M Mahowald, v1– and v2–periodicity in stable homotopy theory, Amer. J. Math. 103 (1981) 615 MR623131
14 D M Davis, M Mahowald, Ext over the subalgebra A2 of the Steenrod algebra for stunted projective spaces, from: "Current trends in algebraic topology, I" (editors R M Kane, S O Kochman, P S Selick, V P Snaith), CMS Conf. Proc. 2, Amer. Math. Soc. (1982) 297 MR686123
15 P Deligne, M Rapoport, Les schémas de modules de courbes elliptiques, from: "Modular functions of one variable, II" (editors P Deligne, W Kuyk), Lecture Notes in Math. 349, Springer (1973) 143 MR0337993
16 E S Devinatz, M J Hopkins, Homotopy fixed point spectra for closed subgroups of the Morava stabilizer groups, Topology 43 (2004) 1 MR2030586
17 C L Douglas, J Francis, A G Henriques, M A Hill, editors, Topological modular forms, 201, Amer. Math. Soc. (2014) MR3223024
18 P G Goerss, Quasi-coherent sheaves on the moduli stack of formal groups, preprint (2008) arXiv:0802.0996
19 P G Goerss, H W Henn, The Brown–Comenetz dual of the K(2)–local sphere at the prime 3, Adv. Math. 288 (2016) 648 MR3436395
20 P Goerss, H W Henn, M Mahowald, The homotopy of L2V (1) for the prime 3, from: "Categorical decomposition techniques in algebraic topology" (editors G Arone, J Hubbuck, R Levi, M Weiss), Progr. Math. 215, Birkhäuser (2004) 125 MR2039763
21 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
22 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
23 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
24 A G Henriques, The homotopy groups of tmf and of its localizations, from: "Topological modular forms" (editors C L Douglas, J Francis, A G Henriques, M A Hill), Mathematical Surveys and Monographs 201, Amer. Math. Soc. (2014) 189 MR3223024
25 M Hovey, N P Strickland, Morava K–theories and localisation, 666, Amer. Math. Soc. (1999) MR1601906
26 S O Kochman, Stable homotopy groups of spheres: a computer-assisted approach, 1423, Springer (1990) MR1052407
27 J Lubin, J Tate, Formal moduli for one-parameter formal Lie groups, Bull. Soc. Math. France 94 (1966) 49 MR238854
28 A Mathew, The homology of tmf, Homology Homotopy Appl. 18 (2016) 1 MR3515195
29 J Milnor, The Steenrod algebra and its dual, Ann. of Math. 67 (1958) 150 MR99653
30 R M F Moss, Secondary compositions and the Adams spectral sequence, Math. Z. 115 (1970) 283 MR266216
31 D C Ravenel, Localization with respect to certain periodic homology theories, Amer. J. Math. 106 (1984) 351 MR737778
32 D C Ravenel, Complex cobordism and stable homotopy groups of spheres, 121, Academic (1986) MR860042
33 D C Ravenel, Nilpotence and periodicity in stable homotopy theory, 128, Princeton Univ. Press (1992) MR1192553
34 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
35 J Rognes, The Adams spectral sequence, (2012)
36 K Shimomura, The homotopy groups of the L2–localized Toda–Smith spectrum V (1) at the prime 3, Trans. Amer. Math. Soc. 349 (1997) 1821 MR1370651
37 K Shimomura, The homotopy groups of the L2–localized mod 3 Moore spectrum, J. Math. Soc. Japan 52 (2000) 65 MR1727130
38 K Shimomura, X Wang, The homotopy groups π(L2S0) at the prime 3, Topology 41 (2002) 1183 MR1923218
39 K Shimomura, A Yabe, The homotopy groups π(L2S0), Topology 34 (1995) 261 MR1318877
40 J H Silverman, The arithmetic of elliptic curves, 106, Springer (2009) MR2514094
41 H Toda, Composition methods in homotopy groups of spheres, 49, Princeton Univ. Press (1962) MR0143217