Smashing Localizations in Equivariant Stable Homotopy

Christian Carrick

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arXiv · 1909.08771

Smashing Localizations in Equivariant Stable Homotopy

Christian Carrick

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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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Christian Carrick. 2019-09-19. Smashing Localizations in Equivariant Stable Homotopy. https://arxiv.org/abs/1909.08771

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