A NOT-NECESSARILY COMMUTATIVE MAP

John Rognes

This is a correction to the author’s paper [3]. Theorem 1.5 and Corollary 9.6.6 are misleadingly formulated, asserting that there are maps of commutative S-algebras

L_{K(n)}S → L̂_{K(n)}^{MU}MU ⟶^{q} { \atop E(n)} → E_{n} .

What is correct is that each of these four objects is a commutative S-algebra, and the maps L_{K(n)}S → R = L̂_{K(n)}^{MU}MU and R/I = { \atop E(n)} → E_{n} are morphisms in the homotopy category of commutative S-algebras, but q: R → R/I is just a morphism in the homotopy category of (associative) R-algebras, hence also in the homotopy category of S-algebras.

Reading the proof, R/I is constructed as an R-algebra by an appeal to Angeltveit [1]. No conflict with the paper of Johnson and Noel [2] is intended or implied.

References

[1] Vigleik Angeltveit, Topological Hochschild homology and cohomology of A_{∞} ring spectra, Geom. Topol. 12 (2008), no. 2, 987–1032.

[2] Niles Johnson and Justin Noel, For complex orientations preserving power operations, ptypicality is atypical, Topology Appl. 157 (2010), no. 14, 2271–2288.

[3] John Rognes, Galois extensions of structured ring spectra, Mem. Amer. Math. Soc. 192 (2008), no. 898, 1–97.

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