The Segal conjecture for topological Hochschild homology of complex cobordism

Abstract

We study the C_p-equivariant Tate construction on the topological Hochschild homology THH(B) of a symmetric ring spectrum B by relating it to a topological version R_+(B) of the Singer construction, extended by a natural circle action. This enables us to prove that the fixed and homotopy fixed point spectra of THH(B) are p-adically equivalent for B = MU and BP. This generalizes the classical C_p-equivariant Segal conjecture, which corresponds to the case B = S.

Accepted for publication by the Journal of Topology

References in corpus (3)

• The Multiplication on BP
• Homology of E_n Ring Spectra and Iterated THH
• On cyclic fixed points of spectra

Cited by in corpus (6)

• On cyclic fixed points of spectra
• Detecting Periodic Elements in Higher Topological Hochschild Homology
• Cubical and cosimplicial descent
• On $K(1)$-local $\mathrm{TR}$
• The circle action on topological Hochschild homology of complex cobordism and the Brown-Peterson spectrum
• The Segal Conjecture for topological Hochschild homology of the Ravenel spectra