Formal structure of direct image of holonomic $${\mathcal{D}}$$ -modules of exponential type

Roucairol, Céline

doi:10.1007/s00229-007-0113-3

Cited by 19 publications

(4 citation statements)

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“…Recently many mathematicians studied direct images of irregular holonomic Dmodules and obtained precise results. For example, see Heizinger [Hei15], Hien-Roucairol [HR08] and Roucairol [Rou06], [Rou07] etc. Note also that in the case N = 1 Fourier transforms of general holonomic D-modules were precisely studied by many authors such as Bloch-Esnault [BE04], D'Agnolo-Kashiwara [DK17], Mochizuki [Moc10] and Sabbah [Sab08] etc.…”

Section: Introductionmentioning

confidence: 99%

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

Itô

Takeuchi

2020

Can. Math. Bull.

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Section: Introductionmentioning

confidence: 99%

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

Itô

Takeuchi

2020

Can. Math. Bull.

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“…For example, if Y is a disc, it is shown in [21] that any formal meromorphic connection at 0 ∈ Y can be produced as the formalization at the origin of a connection obtained by the procedure of Theorem 1.3(3) for some suitable N on X = Y × P…”

Section: Motivations and Open Questionsmentioning

confidence: 99%

“…Examples of this kind can be obtained by the procedure of [21] with arbitrary complicated irregular singularities.…”

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confidence: 99%

On the Irregular Hodge Filtration of Exponentially Twisted Mixed Hodge modules

Sabbah

2015

Forum math. Sigma

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Given a mixed Hodge module N and a meromorphic function f on a complex manifold, we associate to these data a filtration (the irregular Hodge filtration) on the exponentially twisted holonomic module N ⊗ E f , which extends the construction of Esnault et al. (E 1 -degeneration of the irregular Hodge filtration (with an appendix by Saito), J. reine angew. Math. (2015), doi:10.1515/crelle-2014-0118). We show the strictness of the push-forward filtered D-module through any projective morphism π : X → Y , by using the theory of mixed twistor D-modules of Mochizuki. We consider the example of the rescaling of a regular function f , which leads to an expression of the irregular Hodge filtration of the Laplace transform of the Gauss-Manin systems of f in terms of the Harder-Narasimhan filtration of the Kontsevich bundles associated with f .

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“…In [Rou07] Roucairol examined the formal decomposition of direct images of D-modules in the situation presented above. She determined the exponential factors as well as the rank of the corresponding regular parts appearing in the formal decomposition of N .…”

Section: Theorem 14: There Is An Equivalence Of Categories Between Th...mentioning

confidence: 99%

Stokes Structure and Direct Image of Irregular Singular $\mathcal D$-Modules

Heizinger¹

2015

Preprint

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Formal structure of direct image of holonomic $${\mathcal{D}}$$ -modules of exponential type

Cited by 19 publications

References 4 publications

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

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

On the Irregular Hodge Filtration of Exponentially Twisted Mixed Hodge modules

Stokes Structure and Direct Image of Irregular Singular $\mathcal D$-Modules

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