The 𝛼-family in the 𝐾(2)-local sphere at the prime 2

DOI10.1090/conm/729/14689zbMath1429.55014arXiv1712.09083OpenAlexW2948819205MaRDI QIDQ5239151

Agnès Beaudry

Publication date: 22 October 2019

Published in: Homotopy Theory: Tools and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1712.09083

zbMATH Keywords

Adams-Novikov spectral sequencehomotopy fixed point spectral sequence$\alpha$-family$K(2)$-local spherealgebraic duality spectral sequence

Mathematics Subject Classification ID

Localization and completion in homotopy theory (55P60) Adams spectral sequences (55T15) Stable homotopy groups (55Q10) Homotopy groups of spheres (55Q40) Homotopy groups (55Q99) (J)-morphism (55Q50) (v_n)-periodicity (55Q51)

Cites Work

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• The homotopy groups of \(S_{E(2)}\) at \(p\geq 5\) revisited
• Towards the homotopy of the \(K(2)\)-local Moore spectrum at \(p=2\)
• The Brown-Comenetz dual of the \(K(2)\)-local sphere at the prime 3
• The algebraic duality resolution at \(p= 2\)
• Topological modular forms of level 3
• Periodic phenomena in the Adams-Novikov spectral sequence
• The Adams-Novikov \(E_2\)-term for computing \(\pi_*(L_2 V(0))\) at the prime 2
• Homotopy fixed point spectra for closed subgroups of the Morava stabilizer groups.
• 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 groups of the \(L_2\)-localized mod 3 Moore spectrum
• Chromatic splitting for the \(K(2)\)-local sphere at \(p=2\)
• Towards the \(K(2)\)-local homotopy groups of \(Z\)
• The rational homotopy of the \(K(2)\)-local sphere and the chromatic splitting conjecture for the prime 3 and level 2
• The chromatic splitting conjecture at \(n = p = 2\)
• 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
• On the groups \(J(X)\). IV
• On Hopkins’ Picard groups for the prime 3 and chromatic level 2

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