Semiorthogonal decompositions for stacks
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917532122742784 |
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| author | Bu, Chenjing Pădurariu, Tudor Toda, Yukinobu |
| author_facet | Bu, Chenjing Pădurariu, Tudor Toda, Yukinobu |
| contents | We give a systematic construction of semiorthogonal decompositions of derived categories of coherent sheaves on quasi-smooth derived algebraic stacks over $\mathbb{C}$, where the summands are subcategories defined by weight conditions, and the inclusion functors are given by parabolic induction. The summands are indexed by the component lattice of the stack, a central combinatorial structure in intrinsic Donaldson-Thomas theory. As examples, we obtain semiorthogonal decompositions for moduli stacks of semistable $G$-bundles or $G$-Higgs bundles on a curve, and moduli stacks of de Rham or Betti $G$-local systems on a curve, for reductive groups $G$ not necessarily of type A. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_25976 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Semiorthogonal decompositions for stacks Bu, Chenjing Pădurariu, Tudor Toda, Yukinobu Algebraic Geometry Representation Theory We give a systematic construction of semiorthogonal decompositions of derived categories of coherent sheaves on quasi-smooth derived algebraic stacks over $\mathbb{C}$, where the summands are subcategories defined by weight conditions, and the inclusion functors are given by parabolic induction. The summands are indexed by the component lattice of the stack, a central combinatorial structure in intrinsic Donaldson-Thomas theory. As examples, we obtain semiorthogonal decompositions for moduli stacks of semistable $G$-bundles or $G$-Higgs bundles on a curve, and moduli stacks of de Rham or Betti $G$-local systems on a curve, for reductive groups $G$ not necessarily of type A. |
| title | Semiorthogonal decompositions for stacks |
| topic | Algebraic Geometry Representation Theory |
| url | https://arxiv.org/abs/2605.25976 |