Completion of motivic sheaves
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913806375976960 |
|---|---|
| author | Cisinski, Denis-Charles |
| author_facet | Cisinski, Denis-Charles |
| contents | We study the process of $\ell$-adic completion of motivic sheaves. We observe that, in equal characteristic, when restricted to constructible objets, it is compatible with the six operations. This implies that one can reconstruct $\ell$-adic sheaves of geometric origin over a scheme of finite type over a field from $\ell$-adic cohomology of smooth schemes. In the case of finite fields, this includes perverse $\ell$-adic sheaves of geometric orgin. However, the analogous behaviour fails systematically in mixed characteristic: the reason is that it would imply strong independence of $\ell$ results that can be proven to be too optimistic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_24033 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Completion of motivic sheaves Cisinski, Denis-Charles Algebraic Geometry K-Theory and Homology Number Theory We study the process of $\ell$-adic completion of motivic sheaves. We observe that, in equal characteristic, when restricted to constructible objets, it is compatible with the six operations. This implies that one can reconstruct $\ell$-adic sheaves of geometric origin over a scheme of finite type over a field from $\ell$-adic cohomology of smooth schemes. In the case of finite fields, this includes perverse $\ell$-adic sheaves of geometric orgin. However, the analogous behaviour fails systematically in mixed characteristic: the reason is that it would imply strong independence of $\ell$ results that can be proven to be too optimistic. |
| title | Completion of motivic sheaves |
| topic | Algebraic Geometry K-Theory and Homology Number Theory |
| url | https://arxiv.org/abs/2503.24033 |