The Tate spectrum \(v_ n\)-periodic complex oriented theories

DOI10.1007/PL00004264zbMath0849.55005OpenAlexW3196817075MaRDI QIDQ1906887

Hal Sadofsky, John P. C. Greenlees

Publication date: 21 March 1996

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/174891

zbMATH Keywords

periodic homologyTate spectrumMahowald's root invariantperiodic homotopyintegral Morava \(K\)-theoryMorava \(K\)-theory spectrum

Mathematics Subject Classification ID

Connective (K)-theory, cobordism (19L41) Generalized (extraordinary) homology and cohomology theories in algebraic topology (55N20)

Related Items (24)

Tate cohomology in commutative algebra ⋮ Factoring 2\(^{k}\) on stunted projective spectra and the root invariant ⋮ Ambidexterity in chromatic homotopy theory ⋮ Derived induction and restriction theory ⋮ Dualizing spheres for compact \(p\)-adic analytic groups and duality in chromatic homotopy ⋮ Detecting and describing ramification for structured ring spectra ⋮ A short proof of telescopic Tate vanishing ⋮ Higher semiadditive Grothendieck-Witt theory and the 𝐾(1)-local sphere ⋮ Topology. Abstracts from the workshop held July 24--30, 2022 ⋮ Orbifold bordism and duality for finite orbispectra ⋮ Spectral Algebra Models of Unstable $$v_n$$-Periodic Homotopy Theory ⋮ Brown–Peterson cohomology from Morava -theory ⋮ Real connective K-theory and the quaternion group ⋮ The Balmer spectrum of the equivariant homotopy category of a finite abelian group ⋮ Goodwillie Approximations to Higher Categories ⋮ Tate cohomology lowers chromatic Bousfield classes ⋮ Ambidexterity and height ⋮ Root invariants in the Adams spectral sequence ⋮ Completions of Z\(/(p)\)-Tate cohomology of periodic spectra ⋮ Picard groups and duality for real Morava \(E\)-theories ⋮ Gross–Hopkins duals of higher real K–theory spectra ⋮ On the Balmer spectrum for compact Lie groups ⋮ Tate blueshift and vanishing for real oriented cohomology theories ⋮ Analogs of Dirichlet \(L\)-functions in chromatic homotopy theory

Cites Work

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• Equivariant stable homotopy and Segal's Burnside ring conjecture
• Nilpotence and stable homotopy theory. I
• The Boolean algebra of spectra
• The root invariant and \(v_ 1\)-periodic families
• Small ring spectra
• BP operations and Morava's extraordinary K-theories
• Cobordism theories of unitary manifolds with singularities and formal group laws
• \(\nu_n\) telescopes and the Adams spectral sequence
• Periodic Phenomena in the Classical Adams Spectral Sequence
• The spectrum (P ⋀ bo) _−∞
• Liftings of formal groups and the Artinian completion of BP
• The Spectrum (P ∧BP〈2 〉) -∞
• Root Invariants and Periodicity in Stable Homotopy Theory
• On conjectures of Mahowald, Segal and Sullivan
• On Bordism Theory of Manifolds with Singularities.
• Stable Homotopy Theory is not Self-Dual
• Nilpotence and stable homotopy theory. II

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