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- W2120109893 abstract "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 $f:Xto Y$), and may be of some intrinsic interest." @default.
- W2120109893 created "2016-06-24" @default.
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- W2120109893 date "2007-07-12" @default.
- W2120109893 modified "2023-09-27" @default.
- W2120109893 title "Algebraic Connections vs. Algebraic {$cD$}-modules: inverse and direct images" @default.
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