Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.15154 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909118228332544 |
|---|---|
| author | Diao, Hansheng Yao, Zijian |
| author_facet | Diao, Hansheng Yao, Zijian |
| contents | We extend the construction of A$_{\rm inf}$-cohomology by Bhatt-Morrow-Scholze to the context of log $p$-adic formal schemes over a log perfectoid base. In particular, using coordinates, we prove comparison theorems between log A$_{\rm inf}$-cohomology with other $p$-adic cohomology theories, including log de Rham, log (q-)crystalline, log prismatic, and Kummer étale cohomology, as well as the derived A$_{\rm inf}$-cohomology of certain infinite root stacks. Along the way, we define and give a combinatorial characterization of a new class of maps between saturated log schemes, called pseudo-saturated maps, which is of independent interest. They are related to (and slightly weaker than) the notion of quasi-saturated maps and maps of Cartier type studied by Tsuji. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_15154 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Logarithmic A$_{\rm inf}$-cohomology Diao, Hansheng Yao, Zijian Number Theory Algebraic Geometry We extend the construction of A$_{\rm inf}$-cohomology by Bhatt-Morrow-Scholze to the context of log $p$-adic formal schemes over a log perfectoid base. In particular, using coordinates, we prove comparison theorems between log A$_{\rm inf}$-cohomology with other $p$-adic cohomology theories, including log de Rham, log (q-)crystalline, log prismatic, and Kummer étale cohomology, as well as the derived A$_{\rm inf}$-cohomology of certain infinite root stacks. Along the way, we define and give a combinatorial characterization of a new class of maps between saturated log schemes, called pseudo-saturated maps, which is of independent interest. They are related to (and slightly weaker than) the notion of quasi-saturated maps and maps of Cartier type studied by Tsuji. |
| title | Logarithmic A$_{\rm inf}$-cohomology |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2402.15154 |