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arXiv · 2604.10869

Putting the Brauer back in Brauer-Picard

Sean Sanford
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Abstract

We establish a 6-term left exact sequence, involving Galois cohomology of the base field $\mathbb K$, and the Brauer-Picard groupoid of a fusion category. This generalizes a result of Etingof, Nikshych, and Ostrik to the setting where $\mathbb K$ is not algebraically closed. Following their example, we use this exact sequence to compute examples of graded extensions of fusion categories over $\mathbb R$. Along the way, we establish several structural theorems regarding the duality morphisms for a fusion category as an object in the 4-category of braided tensor categories. The paper ends with a speculative look at a potential higher categorical explanation of the main result.

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Sean Sanford. 2026-04-13. Putting the Brauer back in Brauer-Picard. https://arxiv.org/abs/2604.10869

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