Abstract
We study how smashing Bousfield localizations behave under various equivariant functors. We show that the analogs of the smash product and chromatic convergence theorems for the Real Johnson–Wilson theories E_{mathbb {R}}(n) hold only after Borel completion. We establish analogous results for the C_{2^n}-equivariant Johnson–Wilson theories constructed by Beaudry, Hill, Shi, and Zeng. We show that induced localizations upgrade the available norms for an N_infty -algebra, and we determine which new norms appear. Finally, we explore generalizations of our results on smashing localizations in the context of a quasi-Galois extension of E_infty -rings.
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