A note on the Segal conjecture for large objects

2024/03/11 by Burklund, Robert, Subramanian, Vignesh
#Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2403.06724

Abstract

The Segal conjecture for C_p (as proved by Lin and Gunawardena) asserts that the canonical map from the p-complete sphere spectrum to the Tate construction for the trivial action of C_p on the p-complete sphere spectrum is an isomorphism. In this article we extend the collection of spectra for which the canonical map X → X^tC_p is known to be an isomorphism to include any p-complete, bounded below spectrum whose mod p homology, viewed a module over the Steenrod algebra, is complete with respect to the maximal ideal I ⊆ A.

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