Derived equivalences for chain complexes with support
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866912907417092096 |
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| author | Krishnamoorthy, Ganapathy Sane, Sarang |
| author_facet | Krishnamoorthy, Ganapathy Sane, Sarang |
| contents | For a Serre subcategory $\mathscr L$ and a resolving subcategory $\mathscr A$ of an abelian category, we show that the derived equivalence $D^b(\overline{\mathscr A} \cap \mathscr L) \simeq D^b_{\mathscr L}(\mathscr A)$ holds under certain conditions. We apply this to obtain derived equivalences in the contexts of chain complexes of graded modules or coherent sheaves, with finite $\mathscr A$-dimension, supported on closed sets having eventually finite $\mathscr A$-dimension. Using this, we obtain descriptions of the homotopy fibers in (hermitian) K theory of the restriction maps to certain open sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_16729 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Derived equivalences for chain complexes with support Krishnamoorthy, Ganapathy Sane, Sarang Category Theory Commutative Algebra Algebraic Geometry 18G80 (Primary), 13D05, 14F08, 18G20 (Secondary) For a Serre subcategory $\mathscr L$ and a resolving subcategory $\mathscr A$ of an abelian category, we show that the derived equivalence $D^b(\overline{\mathscr A} \cap \mathscr L) \simeq D^b_{\mathscr L}(\mathscr A)$ holds under certain conditions. We apply this to obtain derived equivalences in the contexts of chain complexes of graded modules or coherent sheaves, with finite $\mathscr A$-dimension, supported on closed sets having eventually finite $\mathscr A$-dimension. Using this, we obtain descriptions of the homotopy fibers in (hermitian) K theory of the restriction maps to certain open sets. |
| title | Derived equivalences for chain complexes with support |
| topic | Category Theory Commutative Algebra Algebraic Geometry 18G80 (Primary), 13D05, 14F08, 18G20 (Secondary) |
| url | https://arxiv.org/abs/2601.16729 |