On irregularities of Fourier transforms of regular holonomic D-modules

Abstract

We study Fourier transforms of regular holonomic D-modules. By using the theory of Fourier-Sato transforms of enhanced ind-sheaves developed by Kashiwara-Schapira and D'Agnolo-Kashiwara, a formula for their enhanced solution complexes will be obtained. Moreover we show that some parts of their characteristic cycles and irregularities are expressed by the geometries of the original D-modules.

On Some Topological Properties of Fourier Transforms of Regular Holonomic -Modules

“…The monodromicity of Sol Y (M ∧ ) in Theorem 1.2 follows from its C-constructibility and the R + -conicness (see Lemma 2.1). In this paper we prove Theorem 1.2 by using the theory of enhanced ind-sheaves and our results in [IT18]. In this way, we can also improve Brylinski's Theorem 1.1 as follows.…”

“…Recently in [IT18] the authors studied the Fourier transforms of general regular holonomic D-modules very precisely by using the Riemann-Hilbert correspondence for irregular holonomic D-modules established by D'Agnolo and Kashiwara [DK16] and the Fourier-Sato transforms for enhanced ind-sheaves developed by Kashiwara and Schapira [KS16a]. In this process we found a new proof of Theorem 1.1 (see the proof of Theorem 3.2).…”

D-modules of pure Gaussian type and enhanced ind-sheaves

“…9.8]. It is also given as a corollary of a more general result in [13,Corollary 3.7]. We give a direct proof in the unramified case.…”

“…The theory has since been applied to the study of Stokes phenomena and Fourier-Laplace transforms (see e.g. [4,6,13,21]). Other recent approaches to the study of Fourier transforms of Stokes data have been developed in [24,27].…”