Algebraic Connections vs. Algebraic {$\cD$}-modules: inverse and direct images
| dc.creator | Cailotto, Maurizio | |
| dc.creator | Fiorot, Luisa | |
| dc.date | 2007-07-12 | |
| dc.date.accessioned | 2026-07-07T08:16:13Z | |
| dc.date.available | 2026-07-07T08:16:13Z | |
| dc.description | In the dictionary between the language of (algebraic integrable) connections and that of (algebraic) $\cD$-modules, to compare the definitions of inverse images for connections and $\cD$-modules is easy. But the comparison between direct images for connections (the classical construction of the Gauss-Manin connection for smooth morphisms) and for $\cD$-modules, although known to specialists, has been explicitly proved only recently in a paper of Dimca, Maaref, Sabbah and Saito in 2000, where the authors' main technical tool was M. Saito's equivalence between the derived category of $\cD$-modules and a localized category of differential complexes. The aim of this short paper is to give a simplified summary of the [DMSS] argument, and to propose an alternative proof of this comparison which is simpler, in the sense that it does not use Saito equivalence. Moreover, our alternative strategy of comparison works in a context which is a precursor to the Gauss-Manin connection (at the level of $f^{-1}\cD_Y$-modules, for a morphism $f:X\to Y$), and may be of some intrinsic interest. | |
| dc.description | 11 pages | |
| dc.identifier | https://arxiv.org/abs/0707.1748 | |
| dc.identifier | http://arxiv.org/abs/0707.1748 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/133703 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14F10 | |
| dc.title | Algebraic Connections vs. Algebraic {$\cD$}-modules: inverse and direct images | |
| dc.type | text |