Characteristics for $E_{\infty }$ ring spectra

Abstract

We introduce a notion of characteristic for connective $p$-local $E_{\infty }$ ring spectra and study some basic properties. Apart from examples already pointed out by Markus Szymik, we investigate some examples built from Hopf invariant $1$ elements in the stable homotopy groups of spheres and make some conjectures about spectra for which they may be characteristics; these appear to involve hard questions in stable homotopy theory.

Version 5: minor changes; final version to appear the proceedings of the Alpine Algebraic and Applied Topology Conference

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• Power operations in $K$-theory completed at a prime