Integral Artin motives II: Perverse motives and Artin Vanishing Theorem
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917994691559424 |
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| author | Ruimy, Raphaël |
| author_facet | Ruimy, Raphaël |
| contents | In this text, we are mainly interested in the existence of the perverse motivic t-structures on the category of Artin étale motives with integral coefficients. We construct the perverse homotopy t-structure which is the best possible approximation to a perverse t-structure on Artin motives with rational coefficients. The heart of this t-structure has properties similar to those of the category of perverse sheaves and contains the Ayoub-Zucker motive. With integral coefficients, we construct the perverse motivic t-structure on Artin motives when the base scheme is of dimension at most $2$ and show that it cannot exist in dimension $4$. This construction relies notably on a an analogue for Artin motives of the Artin Vanishing Theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_15732 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Integral Artin motives II: Perverse motives and Artin Vanishing Theorem Ruimy, Raphaël Algebraic Geometry In this text, we are mainly interested in the existence of the perverse motivic t-structures on the category of Artin étale motives with integral coefficients. We construct the perverse homotopy t-structure which is the best possible approximation to a perverse t-structure on Artin motives with rational coefficients. The heart of this t-structure has properties similar to those of the category of perverse sheaves and contains the Ayoub-Zucker motive. With integral coefficients, we construct the perverse motivic t-structure on Artin motives when the base scheme is of dimension at most $2$ and show that it cannot exist in dimension $4$. This construction relies notably on a an analogue for Artin motives of the Artin Vanishing Theorem. |
| title | Integral Artin motives II: Perverse motives and Artin Vanishing Theorem |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2504.15732 |