Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.02922 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915031261642752 |
|---|---|
| author | Fernando, Ravi |
| author_facet | Fernando, Ravi |
| contents | The saturated de Rham-Witt complex, introduced by Bhatt-Lurie-Mathew, is a variant of the classical de Rham-Witt complex which provides a conceptual simplification of the construction and which is expected to produce better results for non-smooth varieties. In this paper, we introduce a generalization of the saturated de Rham-Witt complex which allows coefficients in a unit-root $F$-crystal. We define our complex by a universal property in a category of so-called de Rham-Witt modules. We prove a number of results about it, including existence, quasicoherence, and comparisons to the de Rham-Witt complex of Bhatt-Lurie-Mathew and (in the smooth case) to crystalline cohomology and the classical de Rham-Witt complex with coefficients. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_02922 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Saturated de Rham-Witt complexes with unit-root coefficients Fernando, Ravi Algebraic Geometry 14F30 The saturated de Rham-Witt complex, introduced by Bhatt-Lurie-Mathew, is a variant of the classical de Rham-Witt complex which provides a conceptual simplification of the construction and which is expected to produce better results for non-smooth varieties. In this paper, we introduce a generalization of the saturated de Rham-Witt complex which allows coefficients in a unit-root $F$-crystal. We define our complex by a universal property in a category of so-called de Rham-Witt modules. We prove a number of results about it, including existence, quasicoherence, and comparisons to the de Rham-Witt complex of Bhatt-Lurie-Mathew and (in the smooth case) to crystalline cohomology and the classical de Rham-Witt complex with coefficients. |
| title | Saturated de Rham-Witt complexes with unit-root coefficients |
| topic | Algebraic Geometry 14F30 |
| url | https://arxiv.org/abs/2406.02922 |