On Irregularities of Fourier Transforms of Regular Holonomic D-Modules
Yohei Ito, Kiyoshi Takeuchi
TL;DR
This paper investigates the Fourier transforms of regular holonomic D-modules, deriving formulas for their enhanced solutions and linking their irregularities to the original modules' geometries.
Contribution
It introduces a new formula for the enhanced solution complexes of Fourier-transformed D-modules using advanced sheaf theory.
Findings
Formulas for enhanced solution complexes of Fourier-transformed D-modules
Expression of irregularities via original D-modules' geometries
Connections between characteristic cycles and Fourier transforms
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.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Nonlinear Waves and Solitons · Algebraic structures and combinatorial models