On the Nori and Hodge realisations of Voevodsky motives
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866909845055078400 |
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| author | Tubach, Swann |
| author_facet | Tubach, Swann |
| contents | We show that the derived category of perverse Nori motives and mixed Hodge modules are the derived categories of their constructible hearts. This enables us to construct $\infty$-categorical lifts of the six operations and therefore to obtain realisation functors from the category of Voevodsky étale motives to the derived categories of perverse Nori motives and mixed Hodge modules that commute with the operations. We give a proof that the realisation induces an equivalence of categories between Artin motives in the category of étale motives and Artin motives in the derived category of Nori motives. We also prove that if a motivic $t$-structure exists then Voevodsky étale motives and the derived category of perverse Nori motives are equivalent. Finally we give a presentation of the indization of the derived category of perverse Nori motives as a category of modules in Voevodsky étale motives that gives a continuity result for perverse Nori motives. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2309_11999 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the Nori and Hodge realisations of Voevodsky motives Tubach, Swann Algebraic Geometry Number Theory 14F42, 14F25, 18G80, 14C15 We show that the derived category of perverse Nori motives and mixed Hodge modules are the derived categories of their constructible hearts. This enables us to construct $\infty$-categorical lifts of the six operations and therefore to obtain realisation functors from the category of Voevodsky étale motives to the derived categories of perverse Nori motives and mixed Hodge modules that commute with the operations. We give a proof that the realisation induces an equivalence of categories between Artin motives in the category of étale motives and Artin motives in the derived category of Nori motives. We also prove that if a motivic $t$-structure exists then Voevodsky étale motives and the derived category of perverse Nori motives are equivalent. Finally we give a presentation of the indization of the derived category of perverse Nori motives as a category of modules in Voevodsky étale motives that gives a continuity result for perverse Nori motives. |
| title | On the Nori and Hodge realisations of Voevodsky motives |
| topic | Algebraic Geometry Number Theory 14F42, 14F25, 18G80, 14C15 |
| url | https://arxiv.org/abs/2309.11999 |