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

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.

10 pages

References in corpus (4)

• Stability conditions in families
• Virtual fundamental classes of derived stacks I
• Intersection theories of coherent sheaf stacks and virtual pull-backs via semi-perfect obstruction theories
• The Intrinsic Normal Cone For Artin Stacks