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arXiv · 1905.06830

Virtual classes of $\mathbb{G}_\text{m}$-gerbes

F. Qu
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Abstract

We show that a perfect obstruction theory for a $\mathbb{G}_\text{m}$-gerbe determines a semi-perfect obstruction theory for its base, which is perfect if the gerbe is quasi-compact and affine-pointed. These results streamline the construction of a semi-perfect obstruction theory for the base, and allow us to relate virtual classes of the gerbe and its base.

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F. Qu. 2019-05-16. Virtual classes of $\mathbb{G}_\text{m}$-gerbes. https://doi.org/10.1007/s00229-020-01245-8

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