A generalized Bondal-Orlov full faithfulness criterion for Deligne-Mumford stacks
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914790317752320 |
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| author | Hall, Jack Priver, Kyle |
| author_facet | Hall, Jack Priver, Kyle |
| contents | 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 $Φ_K \colon \mathsf{D}^b_{\mathsf{Coh}}(X) \to \mathsf{D}^b_{\mathsf{Coh}}(Y)$ be the resulting Fourier-Mukai functor. There is a well-known criterion due to Bondal-Orlov for $Φ_K$ to be fully faithful. This criterion was recently extended to smooth Deligne-Mumford stacks with projective coarse moduli schemes by Lim-Polischuk. We extend this to all smooth, proper Deligne-Mumford 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). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_06229 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A generalized Bondal-Orlov full faithfulness criterion for Deligne-Mumford stacks Hall, Jack Priver, Kyle Algebraic Geometry Primary 14F06, 14F08, secondary 14A20 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 $Φ_K \colon \mathsf{D}^b_{\mathsf{Coh}}(X) \to \mathsf{D}^b_{\mathsf{Coh}}(Y)$ be the resulting Fourier-Mukai functor. There is a well-known criterion due to Bondal-Orlov for $Φ_K$ to be fully faithful. This criterion was recently extended to smooth Deligne-Mumford stacks with projective coarse moduli schemes by Lim-Polischuk. We extend this to all smooth, proper Deligne-Mumford 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). |
| title | A generalized Bondal-Orlov full faithfulness criterion for Deligne-Mumford stacks |
| topic | Algebraic Geometry Primary 14F06, 14F08, secondary 14A20 |
| url | https://arxiv.org/abs/2405.06229 |