Hitchin map for the moduli space of $Λ$-modules in positive characteristic
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2023
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866916192740966400 |
|---|---|
| author | Alfaya, David Pauly, Christian |
| author_facet | Alfaya, David Pauly, Christian |
| contents | Building on Simpson's original definition over the complex numbers, we introduce the notion of restricted sheaf $Λ$ of rings of differential operators on a variety defined over a field of positive characteristic. We define the notion of $p$-curvature for $Λ$-modules and the analogue of the Hitchin map on the moduli space of $Λ$-modules. We show that under certain conditions this Hitchin map descends under the Frobenius map of the underlying variety and we give examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_02359 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hitchin map for the moduli space of $Λ$-modules in positive characteristic Alfaya, David Pauly, Christian Algebraic Geometry 14D20, 14G17 Building on Simpson's original definition over the complex numbers, we introduce the notion of restricted sheaf $Λ$ of rings of differential operators on a variety defined over a field of positive characteristic. We define the notion of $p$-curvature for $Λ$-modules and the analogue of the Hitchin map on the moduli space of $Λ$-modules. We show that under certain conditions this Hitchin map descends under the Frobenius map of the underlying variety and we give examples. |
| title | Hitchin map for the moduli space of $Λ$-modules in positive characteristic |
| topic | Algebraic Geometry 14D20, 14G17 |
| url | https://arxiv.org/abs/2303.02359 |