ar X iv : 1 30 3 . 44 79 v 1 [ m at h . A T ] 1 9 M ar 2 01 3 EQUIVARIANT MULTIPLICATIVE
نویسنده
چکیده
This paper concerns a subtle issue that arises when attempting to invert element in the homotopy groups of equivariant commutative (E∞) rings. It arose for the authors in [5], as part of the construction of the spectrum there denoted Ω, and was called to our attention when Justin Noel asked us, “how do you know you can do that?” To set the stage, let G be a finite group, and R a G-equivariant commutative ring, by which we mean and equivariant E∞ ring spectrum. We suppose given a subset S ⊂ π ∗ R. Question 1. Can one form an equivariant commutative ring SR? Example 2. Take G = Z/2, R = S, and S = {2} ⊂ π0S . In this case Noel’s question becomes, “is it possible to invert 2 in equivariant stable homotopy theory?”
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