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arXiv · 1312.7316

On the relative dual of an $S^1$-gerbe over an orbifold

Ilya Shapiro·Xiang Tang·Hsian-Hua Tseng
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Abstract

We construct a new effective orbifold $\widehat{\Y}$ with an $S^1$-gerbe $c$ to study an $S^1$-gerbe $\mathfrak{t}$ on a $G$-gerbe $\Y$ over an orbifold $\B$. We view the former as the relative dual, relative to $\B$, of the latter. We show that the two pairs $(\Y, \mathfrak{t})$ and $(\widehat{\Y}, c)$ have isomorphic categories of sheaves, and also the associated twisted groupoid algebras are Morita equivalent. As a corollary, the K-theory and cohomology groups of $(\Y, \mathfrak{t})$ and $(\widehat{\Y}, c)$ are isomorphic.

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Ilya Shapiro, Xiang Tang, Hsian-Hua Tseng. 2013-12-27. On the relative dual of an $S^1$-gerbe over an orbifold. https://arxiv.org/abs/1312.7316

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