اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدEnhanced nearby and vanishing cycles in dimension one and Fourier transform
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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.
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