The homotopy groups of \(S_{E(2)}\) at \(p\geq 5\) revisited

DOI10.1016/j.aim.2012.02.023zbMath1256.55004arXiv1002.0807OpenAlexW2114041507MaRDI QIDQ424555

Mark J. Behrens

Publication date: 1 June 2012

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1002.0807

zbMATH Keywords

stable homotopy groups of spheres\(E(2)\)-localizationchromatic filtration

Mathematics Subject Classification ID

Homotopy groups (55Q99) Stable homotopy of spheres (55Q45) (v_n)-periodicity (55Q51)

Related Items (11)

Chromatic splitting for the \(K(2)\)-local sphere at \(p=2\) ⋮ On the Iwasawa theory of the Lubin–Tate moduli space ⋮ The chromatic splitting conjecture at \(n = p = 2\) ⋮ Coalgebraic formal curve spectra and spectral jet spaces ⋮ The telescope conjecture at height 2 and the tmf resolution ⋮ Picard groups of higher real -theory spectra at height ⋮ The Slice Spectral Sequence of a 𝐶₄-Equivariant Height-4 Lubin–Tate Theory ⋮ Exotic Picard groups and chromatic vanishing via the Gross-Hopkins duality ⋮ On homotopy groups of \(E_C^{hG_{24}} \wedge A_1\) ⋮ The 𝛼-family in the 𝐾(2)-local sphere at the prime 2 ⋮ The centralizer resolution of the 𝐾(2)-local sphere at the prime 2

Cites Work

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• On Hopkins' Picard group Pic\(_2\) at the prime 3
• Congruences between modular forms given by the divided \(\beta \) family in homotopy theory
• On the Adams-Novikov spectral sequence and products of \(\beta\)-elements
• Non-triviality of some compositions of \(\beta\)-elements in the stable homotopy of the Moore spaces
• The cohomology of the Morava stabilizer algebras
• Periodic phenomena in the Adams-Novikov spectral sequence
• The homotopy groups \(\pi_ * (L_ 2 S^ 0)\)
• The Adams-Novikov \(E_2\)-term for \(\pi_*(L_2S^0)\) at the prime 2
• The homotopy groups \(\pi_*(L_2 S^0)\) at the prime 3
• The homotopy of the \(K(2)\)-local Moore spectrum at the prime 3 revisited
• A resolution of the \(K(2)\)-local sphere at the prime 3
• Morava 𝐾-theories and localisation
• The rigid analytic period mapping, Lubin-Tate space, and stable homotopy theory

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