Prismatic logarithm and prismatic Hochschild homology via norm
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917770405347328 |
|---|---|
| author | Mao, Zhouhang |
| author_facet | Mao, Zhouhang |
| contents | In this brief note, we present an elementary construction of the first Chern class of Hodge--Tate crystals in line bundles using a refinement of the prismatic logarithm, which should be comparable to the one considered by Bhargav Bhatt. The key to constructing this refinement is Yuri Sulyma's norm on (animated) prisms. We explain the relation of this construction to prismatic Witt vectors, as a generalization of Kaledin's polynomial Witt vectors. We also propose the prismatic Hochschild homology as a noncommutative analogue of prismatic de Rham complex. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_04400 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Prismatic logarithm and prismatic Hochschild homology via norm Mao, Zhouhang Algebraic Geometry Algebraic Topology K-Theory and Homology In this brief note, we present an elementary construction of the first Chern class of Hodge--Tate crystals in line bundles using a refinement of the prismatic logarithm, which should be comparable to the one considered by Bhargav Bhatt. The key to constructing this refinement is Yuri Sulyma's norm on (animated) prisms. We explain the relation of this construction to prismatic Witt vectors, as a generalization of Kaledin's polynomial Witt vectors. We also propose the prismatic Hochschild homology as a noncommutative analogue of prismatic de Rham complex. |
| title | Prismatic logarithm and prismatic Hochschild homology via norm |
| topic | Algebraic Geometry Algebraic Topology K-Theory and Homology |
| url | https://arxiv.org/abs/2409.04400 |