Equivalences of equivariant derived categories

Abstract

We investigate conditions for a Fourier-Mukai transform between derived categories of coherent sheaves on smooth projective stacks endowed with actions by finite groups to lift to the associated equivariant derived categories. As an application we give a condition under which a global quotient stack cannot be derived equivalent to a variety. We also apply our techniques to generalised Kummer stacks and symmetric quotients.

arXiv comment24 pages, comments welcome

References in corpus (13)

• Derived categories of coherent sheaves on abelian varieties and equivalences between them
• Reconstruction of a variety from the derived category and groups of autoequivalences
• New derived symmetries of some hyperkähler varieties
• The Mukai pairing, I: a categorical approach
• On equivariant triangulated categories
• On adjunctions for Fourier-Mukai transforms
• Derived autoequivalences of generalised Kummer varieties
• Fourier-Mukai transforms for quotient varieties
• Linearisations of triangulated categories with respect to finite group actions
• Twisted cohomology of the Hilbert schemes of points on surfaces
• P-functor versions of the Nakajima operators
• Spherical functors on the Kummer surface
• A note on separable functors and monads

Cited by in corpus (8)

• A note on spherical functors
• Universal functors on symmetric quotient stacks of Abelian varieties
• Varieties with $\mathbb{P}$-units
• A note on Fourier-Mukai partners of abelian varieties over positive characteristic fields
• Fano visitors, Fano dimension and orbifold Fano hosts
• Twisted Fourier-Mukai partners of Enriques surfaces
• A descent criterion for equivalences between equivariant derived categories
• Descent of tautological sheaves from Hilbert schemes to Enriques manifolds