Adjoining roots in homotopy theory

Tyler Lawson

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arXiv · 2002.01997

Adjoining roots in homotopy theory

Tyler Lawson

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Abstract

We use a "twisted group algebra" method to constructively adjoin formal radicals $\sqrt[n]{\alpha}$, for $\alpha$ a unit in a commutative ring spectrum or an invertible object in a symmetric monoidal $\infty$-category. We show that this construction is classified by maps from Eilenberg-Mac Lane objects to the unit spectrum, the Picard spectrum, and the Brauer spectrum.

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Tyler Lawson. 2020-02-05. Adjoining roots in homotopy theory. https://arxiv.org/abs/2002.01997

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