Localizing invariants of constructible sheaves
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917287392444416 |
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| author | Bai, Qingyuan Haine, Peter J. |
| author_facet | Bai, Qingyuan Haine, Peter J. |
| contents | Given an open-closed decomposition of the stratifying poset, we construct a new semi-orthogonal decomposition of the $\infty$-category of constructible sheaves on a stratified space admitting an exit-path $\infty$-category. From this we obtain a direct sum decomposition of the localizing invariants of the $\infty$-category of constructible sheaves. Since the $\ast$-pullback to the open stratum in the usual (recollement) semi-orthogonal decomposition is not strongly left adjoint, this splitting does not follow from pure sheaf theory considerations. Instead, the splitting crucially relies on the exodromy equivalence: it implies that on the level of constructible sheaves, the $\ast$-pullback to a closed stratum and the $!$-pushforward from an open stratum admit left adjoints. These new functors provide an additional semi-orthogonal decomposition (with the roles of open and closed reversed) in which the relevant functors are strongly left adjoint. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_12810 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Localizing invariants of constructible sheaves Bai, Qingyuan Haine, Peter J. K-Theory and Homology Algebraic Topology Category Theory Given an open-closed decomposition of the stratifying poset, we construct a new semi-orthogonal decomposition of the $\infty$-category of constructible sheaves on a stratified space admitting an exit-path $\infty$-category. From this we obtain a direct sum decomposition of the localizing invariants of the $\infty$-category of constructible sheaves. Since the $\ast$-pullback to the open stratum in the usual (recollement) semi-orthogonal decomposition is not strongly left adjoint, this splitting does not follow from pure sheaf theory considerations. Instead, the splitting crucially relies on the exodromy equivalence: it implies that on the level of constructible sheaves, the $\ast$-pullback to a closed stratum and the $!$-pushforward from an open stratum admit left adjoints. These new functors provide an additional semi-orthogonal decomposition (with the roles of open and closed reversed) in which the relevant functors are strongly left adjoint. |
| title | Localizing invariants of constructible sheaves |
| topic | K-Theory and Homology Algebraic Topology Category Theory |
| url | https://arxiv.org/abs/2512.12810 |