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arXiv · 1010.5635

The Segal conjecture for topological Hochschild homology of complex cobordism

Sverre Lunøe--Nielsen·John Rognes
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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.

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Sverre Lunøe--Nielsen, John Rognes. 2010-10-27. The Segal conjecture for topological Hochschild homology of complex cobordism. https://doi.org/10.1112/jtopol%2Fjtr015

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