Volume 20, issue 7 (2020)

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Invertible $K(2)$–local $E$–modules in $C_4$–spectra

Agnès Beaudry, Irina Bobkova, Michael Hill and Vesna Stojanoska

Algebraic & Geometric Topology 20 (2020) 3423–3503
Bibliography
1 A Baker, B Richter, Invertible modules for commutative 𝕊–algebras with residue fields, Manuscripta Math. 118 (2005) 99 MR2171294
2 M Behrens, K Ormsby, On the homotopy of Q(3) and Q(5) at the prime 2, Algebr. Geom. Topol. 16 (2016) 2459 MR3572338
3 A J Blumberg, M A Hill, G–symmetric monoidal categories of modules over equivariant commutative ring spectra, Tunis. J. Math. 2 (2020) 237 MR3990819
4 I Bobkova, P G Goerss, Topological resolutions in K(2)–local homotopy theory at the prime 2, J. Topol. 11 (2018) 918 MR3989433
5 D Gepner, T Lawson, Brauer groups and Galois cohomology of commutative ring spectra, preprint (2016) arXiv:1607.01118
6 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
7 J P C Greenlees, J P May, Generalized Tate cohomology, 543, Amer. Math. Soc. (1995) MR1230773
8 J Hahn, X D Shi, Real orientations of Lubin–Tate spectra, Invent. Math. 221 (2020) 731 MR4132956
9 D Heard, G Li, X D Shi, Picard groups and duality for real Morava E–theories, preprint (2018) arXiv:1810.05439
10 D Heard, A Mathew, V Stojanoska, Picard groups of higher real K–theory spectra at height p 1, Compos. Math. 153 (2017) 1820 MR3705278
11 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
12 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
13 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
14 M A Hill, L Meier, The C2–spectrum Tmf1(3) and its invertible modules, Algebr. Geom. Topol. 17 (2017) 1953 MR3685599
15 M A Hill, X D Shi, G Wang, Z Xu, The slice spectral sequence of a C4–equivariant height-4 Lubin–Tate theory, preprint (2018) arXiv:1811.07960
16 A Mathew, V Stojanoska, The Picard group of topological modular forms via descent theory, Geom. Topol. 20 (2016) 3133 MR3590352
17 L S Nave, The Smith–Toda complex V ((p + 1)2) does not exist, Ann. of Math. 171 (2010) 491 MR2630045
18 J R Ullman, On the regular slice spectral sequence, PhD thesis, Massachusetts Institute of Technology (2013)