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

Differential systems of pure Gaussian type are examples of D-modules on the complex projective line with an irregular singularity at infinity, and as such are subject to the Stokes phenomenon. We employ the theory of enhanced ind-sheaves and the Riemann–Hilbert correspondence for holonomic D-modules...

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Bibliographic Details
Published inManuscripta mathematica Vol. 167; no. 3-4; pp. 435 - 467
Main Author Hohl, Andreas
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2022
Springer Nature B.V
Subjects
Algebraic Geometry
Calculus of Variations and Optimal Control; Optimization
Geometry
Laplace transforms
Lie Groups
Mathematics
Mathematics and Statistics
Modules
Number Theory
Sheaves
Topological Groups
44A10
34M40
32C38
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ISSN0025-2611
1432-1785
DOI10.1007/s00229-021-01281-y

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Summary:Differential systems of pure Gaussian type are examples of D-modules on the complex projective line with an irregular singularity at infinity, and as such are subject to the Stokes phenomenon. We employ the theory of enhanced ind-sheaves and the Riemann–Hilbert correspondence for holonomic D-modules of D’Agnolo and Kashiwara to describe the Stokes phenomenon topologically. Using this description, we perform a topological computation of the Fourier–Laplace transform of a D-module of pure Gaussian type in this framework, recovering and generalizing a result of Sabbah.
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ISSN:0025-2611
1432-1785
DOI:10.1007/s00229-021-01281-y