an:07183749
Zbl 07183749
Ito, Yohei; Takeuchi, Kiyoshi
On irregularities of Fourier transforms of regular holonomic \(\mathcal{D}\)-modules
EN
Adv. Math. 366, Article ID 107093, 62 p. (2020).
00448179
2020
j
32C38 32S60 34M35 35A27
\(\mathcal{D}\)-modules; Fourier transforms; irregular singularities
Summary: We study Fourier transforms of regular holonomic \(\mathcal{D}\)-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 \(\mathcal{D}\)-modules.