A Simpson correspondence in positive characteristic
| dc.creator | Gros, Michel | |
| dc.creator | Stum, Bernard Le | |
| dc.creator | Quirós, Adolfo | |
| dc.date | 2008-11-07 | |
| dc.date.accessioned | 2026-07-07T10:16:51Z | |
| dc.date.available | 2026-07-07T10:16:51Z | |
| dc.description | We define the $p^m$-curvature map on the sheaf of differential operators of level $m$ on a scheme of positive characteristic $p$ as dual to some divided power map on infinitesimal neighborhhods. This leads to the notion of $p^m$-curvature on differential modules of level $m$. We use this construction to recover Kaneda's description of a semi-linear Azumaya splitting of the sheaf of differential operators of level $m$. Then, using a lifting modulo $p^2$ of Frobenius, we are able to define a Frobenius map on differential operators of level $m$ as dual to some divided Frobenius on infinitesimal neighborhhods. We use this map to build a true Azumaya splitting of the completed sheaf of differential operators of level $m$ (up to an automorphism of the center). From this, we derive the fact that Frobenius pull back gives, when restricted to quasi-nilpotent objects, an equivalence between Higgs-modules and differential modules of level $m$. We end by explaining the relation with related work of Ogus-Vologodski and van der Put in level zero as well as Berthelot's Frobenius descent. | |
| dc.identifier | https://arxiv.org/abs/0811.1168 | |
| dc.identifier | http://arxiv.org/abs/0811.1168 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/173654 | |
| dc.subject | Algebraic Geometry | |
| dc.title | A Simpson correspondence in positive characteristic | |
| dc.type | text |