论文标题
在附近增强并消失的周期在尺寸一和傅立叶变换中
Enhanced nearby and vanishing cycles in dimension one and Fourier transform
论文作者
论文摘要
增强的IND-SHAVE为不规则的Riemann-Hilbert对应提供了合适的框架。在本文中，我们在附近的周期中提供了一些精确度，以增强尺寸的不正当物体。作为应用程序，我们给出以下事实的拓扑证明。令$ \ Mathcal M $为载体线上的自动代数$ \ Mathcal d $ - 模块，并用$ {}^{\ Mathsf {l}} \ Mathcal m $ MATHCAL M $表示其傅立叶 - 宽带变换。对于Aggine Line上的点$ A $，用$ \ ell_a $表示双载体线上的相应线性函数。然后，$ a $的$ \ mathcal m $的消失周期与$ {}^{}^{\ mathsf {l}} \ Mathcal m $的$ \ ell_a $的分级成分同构。
Enhanced ind-sheaves provide a suitable framework for the irregular Riemann-Hilbert correspondence. In this paper, we give some precisions on nearby and vanishing cycles for enhanced perverse objects in dimension one. As an application, we give a topological proof of the following fact. Let $\mathcal M$ be a holonomic algebraic $\mathcal D$-module on the affine line, and denote by ${}^{\mathsf{L}}\mathcal M$ its Fourier-Laplace transform. For a point $a$ on the affine line, denote by $\ell_a$ the corresponding linear function on the dual affine line. Then, the vanishing cycles of $\mathcal M$ at $a$ are isomorphic to the graded component of degree $\ell_a$ of the Stokes filtration of ${}^{\mathsf{L}}\mathcal M$ at infinity.
