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| Format: | Preprint |
| Published: |
2026
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| Online Access: | https://arxiv.org/abs/2601.21052 |
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| _version_ | 1866912969098526720 |
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| author | André, Yves |
| author_facet | André, Yves |
| contents | The classical Rees construction (of common use in commutative algebra and Hodge theory) interpolates between filtrations, viewed as ${\mathbb G}_m$-equivariant vector bundles on the affine line, and their associated gradings. Various non-abelian versions have been proposed, where the multiplicative group ${\mathbb G}_m$ is replaced by an arbitrary reductive group. Building on a construction due to P. O'Sullivan, we present a Galois correspondence between quasi-homogeneous spaces and certain monoidal categories, and apply it to monoidal categories of motives with concrete applications to algebraic cycles. In particular, we give a new proof and generalization of the Clozel-Deligne theorem about numerical equivalence on abelian varieties over finite fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_21052 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Non-abelian Rees construction and pure motives André, Yves Algebraic Geometry Category Theory Number Theory 14A30, 14C15, 14C99 The classical Rees construction (of common use in commutative algebra and Hodge theory) interpolates between filtrations, viewed as ${\mathbb G}_m$-equivariant vector bundles on the affine line, and their associated gradings. Various non-abelian versions have been proposed, where the multiplicative group ${\mathbb G}_m$ is replaced by an arbitrary reductive group. Building on a construction due to P. O'Sullivan, we present a Galois correspondence between quasi-homogeneous spaces and certain monoidal categories, and apply it to monoidal categories of motives with concrete applications to algebraic cycles. In particular, we give a new proof and generalization of the Clozel-Deligne theorem about numerical equivalence on abelian varieties over finite fields. |
| title | Non-abelian Rees construction and pure motives |
| topic | Algebraic Geometry Category Theory Number Theory 14A30, 14C15, 14C99 |
| url | https://arxiv.org/abs/2601.21052 |