Download this article
Download this article For screen
For printing
Recent Issues

Volume 24
Issue 9, 4731–5219
Issue 8, 4139–4730
Issue 7, 3571–4137
Issue 6, 2971–3570
Issue 5, 2389–2970
Issue 4, 1809–2387
Issue 3, 1225–1808
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 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
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