Lisse extensions of weaves
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910903200382976 |
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| author | Khan, Adeel A. |
| author_facet | Khan, Adeel A. |
| contents | Any sheaf theory on schemes extends canonically to Artin stacks via a procedure called lisse extension. In this paper we show that lisse extension preserves the formalism of Grothendieck's six operations: more precisely, the lisse extension of a weave on schemes determines a weave on (higher) Artin stacks. The setup is general enough to apply to the stable motivic homotopy category with the six functor formalism of Voevodsky-Ayoub-Cisinski-Deglise, for instance, and is not specific to algebraic geometry: for example, it also applies to sheaves of spectra on topological stacks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_04114 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lisse extensions of weaves Khan, Adeel A. Algebraic Geometry Algebraic Topology Any sheaf theory on schemes extends canonically to Artin stacks via a procedure called lisse extension. In this paper we show that lisse extension preserves the formalism of Grothendieck's six operations: more precisely, the lisse extension of a weave on schemes determines a weave on (higher) Artin stacks. The setup is general enough to apply to the stable motivic homotopy category with the six functor formalism of Voevodsky-Ayoub-Cisinski-Deglise, for instance, and is not specific to algebraic geometry: for example, it also applies to sheaves of spectra on topological stacks. |
| title | Lisse extensions of weaves |
| topic | Algebraic Geometry Algebraic Topology |
| url | https://arxiv.org/abs/2501.04114 |