论文标题
单粒子混合霍奇模块的描述
A description of monodromic mixed Hodge modules
论文作者
论文摘要
对于平滑的代数品种$ x $，$ x \ times \ times \ mathbb {c} $的单元素$ d $ module被分解为$ x $的大约$ d $ modules的直接总和。我们表明，在$ x \ times \ mathbb {c} $上的混合霍奇模块的霍奇过滤的基础$ d $ - 模块也已分解。此外，我们表明，在$ x \ times \ mathbb {c} $上的单粒子混合霍奇模块类别与``胶合数据''的类别之间存在类别等效。作为一种应用程序，我们赋予了带有混合Hodge模块结构的单粒子混合杂货模块的基础$ d $模块的傅立叶宽段转换。
For a smooth algebraic variety $X$, a monodromic $D$-module on $X\times \mathbb{C}$ is decomposed into a direct sum of some $D$-modules on $X$. We show that the Hodge filtration of a mixed Hodge module on $X\times \mathbb{C}$ whose underlying $D$-module is monodromic is also decomposed. Moreover, we show that there is an equivalence of categories between the category of monodromic mixed Hodge modules on $X\times \mathbb{C}$ and the category of ``gluing data''. As an application, we endow the Fourier-Laplace transformation of the underlying $D$-module of a monodromic mixed Hodge module with a mixed Hodge module structure.
