Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2312.01825 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912450744418304 |
|---|---|
| author | Kahn, Bruno |
| author_facet | Kahn, Bruno |
| contents | We give necessary conditions for a category fibred in pseudo-abelian additive categories over the classifying topos of a profinite group to be a stack; these conditions are sufficient when the coefficients are $\mathbf{Q}$-linear. This applies to pure motives over a field in the sense of Grothendieck, Deligne-Milne and André, to mixed motives in the sense of Nori and to several motivic categories considered in arXiv:1506.08386 [math.AG]. We also give a simple proof of the exactness of a sequence of motivic Galois groups under a Galois extension of the base field, which applies to all the above (Tannakian) situations. Finally, we clarify the construction of the categories of Chow-Lefschetz motives given in arXiv:2302.08327 [math.AG] and simplify the computation of their motivic Galois group in the numerical case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_01825 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Galois descent for motivic theories Kahn, Bruno Algebraic Geometry Category Theory 18F20, 18M25, 14C15 We give necessary conditions for a category fibred in pseudo-abelian additive categories over the classifying topos of a profinite group to be a stack; these conditions are sufficient when the coefficients are $\mathbf{Q}$-linear. This applies to pure motives over a field in the sense of Grothendieck, Deligne-Milne and André, to mixed motives in the sense of Nori and to several motivic categories considered in arXiv:1506.08386 [math.AG]. We also give a simple proof of the exactness of a sequence of motivic Galois groups under a Galois extension of the base field, which applies to all the above (Tannakian) situations. Finally, we clarify the construction of the categories of Chow-Lefschetz motives given in arXiv:2302.08327 [math.AG] and simplify the computation of their motivic Galois group in the numerical case. |
| title | Galois descent for motivic theories |
| topic | Algebraic Geometry Category Theory 18F20, 18M25, 14C15 |
| url | https://arxiv.org/abs/2312.01825 |