A note on cohomological boundedness for $F$-divided sheaves and $\mathcal{D}$-modules
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866915594315497472 |
|---|---|
| author | Yi, Xiaodong |
| author_facet | Yi, Xiaodong |
| contents | Let $X$ be a smooth proper scheme over an algebraically closed field $k$ in characteristic $p$. In this short note, by interpreting $\mathcal{D}_{X}$-modules as $F$-divided sheaves and establishing a cohomological boundedness property for $F$-divided sheaves, we prove that any $\mathcal{O}_{X}$-coherent $\mathcal{D}_{X}$-module has finite dimensional $\mathcal{D}_{X}$-module cohomology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_23526 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on cohomological boundedness for $F$-divided sheaves and $\mathcal{D}$-modules Yi, Xiaodong Algebraic Geometry Let $X$ be a smooth proper scheme over an algebraically closed field $k$ in characteristic $p$. In this short note, by interpreting $\mathcal{D}_{X}$-modules as $F$-divided sheaves and establishing a cohomological boundedness property for $F$-divided sheaves, we prove that any $\mathcal{O}_{X}$-coherent $\mathcal{D}_{X}$-module has finite dimensional $\mathcal{D}_{X}$-module cohomology. |
| title | A note on cohomological boundedness for $F$-divided sheaves and $\mathcal{D}$-modules |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2506.23526 |