论文标题
单粒子混合霍奇模块和不规则霍奇过滤的霍奇过滤
The Hodge filtration of a monodromic mixed Hodge module and the irregular Hodge filtration
论文作者
论文摘要
对于平滑代数品种$ x $上的代数矢量捆绑包$ e $，$ e $上的monodromic $ d $ module被分解为$ x $的一些$ o $ - 模块的直接总和。我们表明，相对于基础$ d $模块的分解，单粒混合杂货模块的Hodge过滤分解了。通过使用此结果，我们赋予了基础$ d $ d $ -Module $ m $ m $ m $ m $ m $ m $ m $ m $ m $ m $ m $ m $ y monodromic混合杂货模块，我们将使用此结果。此外，我们在$ m^{\ wedge} $上描述了不规则的Hodge过滤，并表明它与Hodge过滤相吻合。
For an algebraic vector bundle $E$ over a smooth algebraic variety $X$, a monodromic $D$-module on $E$ is decomposed into a direct sum of some $O$-modules on $X$. We show that the Hodge filtration of a monodromic mixed Hodge module is decomposed with respect to the decomposition of the underlying $D$-module. By using this result, we endow the Fourier-Laplace transform $M^{\wedge}$ of the underlying $D$-module $M$ of a monodromic mixed Hodge module with a mixed Hodge module structure. Moreover, we describe the irregular Hodge filtration on $M^{\wedge}$ concretely and show that it coincides with the Hodge filtration at all integer indices.
