A generalized BondalOrlov full faithfulness criterion for DeligneMumford stacks
Abstract
Let $X$, $Y$ be smooth projective varieties over $\mathbf{C}$. Let $K$ be a bounded complex of coherent sheaves on $X\times Y$ and let $\Phi_K \colon \mathsf{D}^b_{\mathsf{Coh}}(X) \to \mathsf{D}^b_{\mathsf{Coh}}(Y)$ be the resulting FourierMukai functor. There is a wellknown criterion due to BondalOrlov for $\Phi_K$ to be fully faithful. This criterion was recently extended to smooth DeligneMumford stacks with projective coarse moduli schemes by LimPolischuk. We extend this to all smooth, proper DeligneMumford stacks over arbitrary fields of characteristic $0$. Along the way, we establish a number of foundational results for bounded derived categories of proper and tame morphisms of noetherian algebraic stacks (e.g., coherent duality).
 Publication:

arXiv eprints
 Pub Date:
 May 2024
 DOI:
 10.48550/arXiv.2405.06229
 arXiv:
 arXiv:2405.06229
 Bibcode:
 2024arXiv240506229H
 Keywords:

 Mathematics  Algebraic Geometry;
 Primary 14F06;
 14F08;
 secondary 14A20