English

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

Algebraic Geometry 2020-09-22 v2

Abstract

We show that a perfect obstruction theory for a Gm\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.

Keywords

Cite

@article{arxiv.1905.06830,
  title  = {Virtual classes of $\mathbb{G}_\text{m}$-gerbes},
  author = {F. Qu},
  journal= {arXiv preprint arXiv:1905.06830},
  year   = {2020}
}

Comments

10 pages

R2 v1 2026-06-23T09:08:56.204Z