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摘要翻译：
在（代数可积）连接语言和（代数）$\cd$-模语言之间的字典中，比较连接和$\cd$-模的逆像定义是很容易的。但是，关于连接（光滑态射的Gauss-Manin连接的经典构造）和$\cd$-模的直接映象之间的比较，虽然为专家所知，但直到最近才在Dimca、Maaref、Sabbah和Saito在2000年的一篇论文中得到明确证明，其中作者的主要技术工具是M.Saito在$\cd$-模的导出范畴和微分复形的局部范畴之间的等价性。这篇简短的论文的目的是对[DMSS]论点作一个简化的总结，并提出一种更简单的这种比较的替代证明，因为它不使用Saito等价。此外，我们的替代比较策略在Gauss-Manin连接的前驱上下文中工作（对于态射$f:x\到y$而言，在$f^{-1}\cd_y$-模的层次上），并且可能具有某种内在的兴趣。
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英文标题：
《Algebraic Connections vs. Algebraic {$\cD$}-modules: inverse and direct
images》
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作者：
Maurizio Cailotto, Luisa Fiorot
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最新提交年份：
2007
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
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.
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PDF链接：
https://arxiv.org/pdf/0707.1748
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