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Vanishing lines in chromatic homotopy theory

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Bibliography
1 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
2 A Beaudry, The algebraic duality resolution at p = 2, Algebr. Geom. Topol. 15 (2015) 3653 MR3450774
3 A Beaudry, M A Hill, X D Shi, M Zeng, Models of Lubin–Tate spectra via real bordism theory, Adv. Math. 392 (2021) 108020 MR4313964
4 A Beaudry, P G Goerss, H W Henn, Chromatic splitting for the K(2)-local sphere at p = 2, Geom. Topol. 26 (2022) 377 MR4404881
5 M Behrens, M Mahowald, J D Quigley, The 2-primary Hurewicz image of tmf, Geom. Topol. 27 (2023) 2763 MR4645486
6 P Bhattacharya, H Chatham, On the EO-orientability of vector bundles, J. Topol. 15 (2022) 2017 MR4584584
7 M Bökstedt, I Madsen, Topological cyclic homology of the integers, from: "K-theory", Astérisque 226, Soc. Math. France (1994) 57 MR1317117
8 C Bujard, Finite subgroups of extended Morava stabilizer groups, PhD thesis, Université de Strasbourg (2012) arXiv:1206.1951
9 E S Devinatz, M J Hopkins, Homotopy fixed point spectra for closed subgroups of the Morava stabilizer groups, Topology 43 (2004) 1 MR2030586
10 E S Devinatz, M J Hopkins, J H Smith, Nilpotence and stable homotopy theory, I, Ann. of Math. 128 (1988) 207 MR0960945
11 Z Duan, H J Kong, G Li, Y Lu, G Wang, RO(G)-graded homotopy fixed point spectral sequence for height 2 Morava E-theory, Peking Math. J. (2024)
12 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
13 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
14 J Hahn, X D Shi, Real orientations of Lubin–Tate spectra, Invent. Math. 221 (2020) 731 MR4132956
15 H W Henn, On finite resolutions of K(n)-local spheres, from: "Elliptic cohomology" (editors H R Miller, D C Ravenel), Lond. Math. Soc. Lect. Note Ser. 342, Cambridge Univ. Press (2007) 122 MR2330511
16 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
17 T Hewett, Finite subgroups of division algebras over local fields, J. Algebra 173 (1995) 518 MR1327867
18 T Hewett, Normalizers of finite subgroups of division algebras over local fields, Math. Res. Lett. 6 (1999) 271 MR1713129
19 M A Hill, C Yarnall, A new formulation of the equivariant slice filtration with applications to Cp-slices, Proc. Amer. Math. Soc. 146 (2018) 3605 MR3803684
20 M A Hill, M J Hopkins, D C Ravenel, On the nonexistence of elements of Kervaire invariant one, Ann. of Math. 184 (2016) 1 MR3505179
21 M A Hill, M J Hopkins, D C Ravenel, The slice spectral sequence for the C4 analog of real K-theory, Forum Math. 29 (2017) 383 MR3619120
22 M A Hill, X D Shi, G Wang, Z Xu, The slice spectral sequence of a C4-equivariant height-4 Lubin–Tate theory, 1429, Amer. Math. Soc. (2023) MR4627086
23 M J Hopkins, J H Smith, Nilpotence and stable homotopy theory, II, Ann. of Math. 148 (1998) 1 MR1652975
24 P Hu, I Kriz, Real-oriented homotopy theory and an analogue of the Adams–Novikov spectral sequence, Topology 40 (2001) 317 MR1808224
25 N Kitchloo, W S Wilson, The ER(n)-cohomology of BO(q) and real Johnson–Wilson orientations for vector bundles, Bull. Lond. Math. Soc. 47 (2015) 835 MR3403965
26 G Li, X D Shi, G Wang, Z Xu, Hurewicz images of real bordism theory and real Johnson–Wilson theories, Adv. Math. 342 (2019) 67 MR3877362
27 J Lurie, Elliptic cohomology, II: Orientations, preprint (2018)
28 A Mathew, L Meier, Affineness and chromatic homotopy theory, J. Topol. 8 (2015) 476 MR3356769
29 J P May, The geometry of iterated loop spaces, 271, Springer (1972) MR0420610
30 L Meier, X D Shi, M Zeng, The localized slice spectral sequence, norms of real bordism, and the Segal conjecture, Adv. Math. 412 (2023) 108804 MR4517348
31 H R Miller, D C Ravenel, W S Wilson, Periodic phenomena in the Adams–Novikov spectral sequence, Ann. of Math. 106 (1977) 469 MR0458423
32 D Quillen, On the formal group laws of unoriented and complex cobordism theory, Bull. Amer. Math. Soc. 75 (1969) 1293 MR0253350
33 D C Ravenel, The non-existence of odd primary Arf invariant elements in stable homotopy, Math. Proc. Cambridge Philos. Soc. 83 (1978) 429 MR0474291
34 D C Ravenel, Nilpotence and periodicity in stable homotopy theory, 128, Princeton Univ. Press (1992) MR1192553
35 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
36 J Rognes, Galois extensions of structured ring spectra: stably dualizable groups, 898, Amer. Math. Soc. (2008) MR2387923
37 J R Ullman, On the regular slice spectral sequence, PhD thesis, Massachusetts Institute of Technology (2013) MR3211466