Bernstein--Sato Theory for D-modules in Positive Characteristic
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913038026670080 |
|---|---|
| author | Takeuchi, Daichi |
| author_facet | Takeuchi, Daichi |
| contents | In this article, we develop a positive characteristic analogue of the Bernstein--Sato theory for holonomic D-modules in the complex setting. We work with D-modules on a Noetherian regular $F$-finite $\mathbb{F}_p$-scheme $X$, and define their Bernstein--Sato roots as $p$-adic integers. When the D-module is the structure sheaf $O_X$, this recovers Bitoun's definition.
When the D-module arises from a locally finitely generated unit $F^e$-module and $X$ is of finite type over an $F$-finite field, we show that the roots are finite and rational, generalizing Bitoun's result. In the course of the proof, we also develop a related theory for Cartier modules. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_14584 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bernstein--Sato Theory for D-modules in Positive Characteristic Takeuchi, Daichi Algebraic Geometry 14F10, 13A35 In this article, we develop a positive characteristic analogue of the Bernstein--Sato theory for holonomic D-modules in the complex setting. We work with D-modules on a Noetherian regular $F$-finite $\mathbb{F}_p$-scheme $X$, and define their Bernstein--Sato roots as $p$-adic integers. When the D-module is the structure sheaf $O_X$, this recovers Bitoun's definition. When the D-module arises from a locally finitely generated unit $F^e$-module and $X$ is of finite type over an $F$-finite field, we show that the roots are finite and rational, generalizing Bitoun's result. In the course of the proof, we also develop a related theory for Cartier modules. |
| title | Bernstein--Sato Theory for D-modules in Positive Characteristic |
| topic | Algebraic Geometry 14F10, 13A35 |
| url | https://arxiv.org/abs/2604.14584 |