25 citations · 171 across the 21 of their papers we have counts for
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On the irregular Riemann-Hilbert correspondence
Andrea D'Agnolo, Masaki Kashiwara
The original Riemann-Hilbert problem asks to find a Fuchsian ordinary differential equation with prescribed singularities and monodromy in the complex line. In the early 1980's Kas…
On a topological counterpart of regularization for holonomic D-modules
Andrea D'Agnolo, Masaki Kashiwara
On a complex manifold, the embedding of the category of regular holonomic D-modules into that of holonomic D-modules has a left quasi-inverse functor $\mathcal{M}\mapsto\mathcal{M}…
Enhanced nearby and vanishing cycles in dimension one and Fourier transform
Andrea D'Agnolo, Masaki Kashiwara
Enhanced ind-sheaves provide a suitable framework for the irregular Riemann-Hilbert correspondence. In this paper, we give some precisions on nearby and vanishing cycles for enhanc…
Enhanced specialization and microlocalization
Andrea D'Agnolo, Masaki Kashiwara
Enhanced ind-sheaves provide a suitable framework for the irregular Riemann-Hilbert correspondence. In this paper, we show how Sato's specialization and microlocalization functors…
Topological computation of some Stokes phenomena on the affine line
Andrea D'Agnolo, Marco Hien, Giovanni Morando +1
Let be a holonomic algebraic -module on the affine line, regular everywhere including at infinity. Malgrange gave a complete description of the Fourier-Lap…
Enhanced perversities
Andrea D'Agnolo, Masaki Kashiwara
The Riemann-Hilbert correspondence embeds the triangulated category of (not necessarily regular) holonomic D-modules into that of -constructible enhanced ind-sheaves. Th…
Riemann-Hilbert correspondence for holonomic D-modules
Andrea D'Agnolo, Masaki Kashiwara
The classical Riemann-Hilbert correspondence establishes an equivalence between the triangulated category of regular holonomic D-modules and that of constructible sheaves. In this…
On a reconstruction theorem for holonomic systems
Andrea D'Agnolo, Masaki Kashiwara
Let X be a complex manifold. The classical Riemann-Hilbert correspondence associates to a regular holonomic system M the C-constructible complex of its holomorphic solutions. Denot…
On the Laplace transform for tempered holomorphic functions
Andrea D'Agnolo
In order to discuss the Fourier-Sato transform of not necessarily conic sheaves, we compensate the lack of homogeneity by adding an extra variable. We can then obtain Paley-Wiener…
Morita classes of microdifferential algebroids
Andrea D'Agnolo, Pietro Polesello
Projective cotangent bundles of complex manifolds are the local models of complex contact manifolds. Such bundles are quantized by the algebra of microdifferential operators (a loc…
On quantization of complex symplectic manifolds
Andrea D'Agnolo, Masaki Kashiwara
Let X be a complex symplectic manifold. By showing that any Lagrangian subvariety has a unique lift to a contactification, we associate to X a triangulated category of regular holo…
A note on quantization of complex symplectic manifolds
Andrea D'Agnolo, Masaki Kashiwara
To a complex symplectic manifold X we associate a canonical quantization algebroid. Our construction is similar to that of Polesello-Schapira's deformation-quantization algebroid,…
Regular holonomic D[[h]]-modules
Andrea D'Agnolo, Stephane Guillermou, Pierre Schapira
We describe the category of regular holonomic modules over the ring D[[h]] of linear differential operators with a formal parameter h. In particular, we establish the Riemann-Hilbe…
Quantization of complex Lagrangian submanifolds
Andrea D'Agnolo, Pierre Schapira
Let be a smooth Lagrangian submanifold of a complex symplectic manifold . We construct twisted simple holonomic modules along in the stack of deformation-quantization mo…
Sheaves and D-modules in integral geometry
Andrea D'Agnolo
Integral geometry deals with those integral transforms which associate to ``functions'' on a manifold their integrals along submanifolds parameterized by another manifold. Basic pr…
Deformation-Quantization of Complex Involutive Submanifolds
Andrea D'Agnolo, Pietro Polesello
The sheaf of rings of WKB operators provides a deformation-quantization of the cotangent bundle to a complex manifold. On a complex symplectic manifold there may not exist a sh…
On twisted microdifferential modules I. Non-existence of twisted wave equations
Andrea D'Agnolo, Pierre Schapira
Using the notion of subprincipal symbol, we give a necessary condition for the existence of twisted D-modules simple along a smooth involutive submanifold of the cotangent bundle t…
Stacks of twisted modules and integral transforms
Andrea D'Agnolo, Pietro Polesello
Stacks were introduced by Grothendieck and Giraud and are, roughly speaking, sheaves of categories. Kashiwara developed the theory of twisted modules, which are objects of stacks l…
On Dwork cohomology and algebraic D-modules
Francesco Baldassarri, Andrea D'Agnolo
After works by Katz, Monsky, and Adolphson-Sperber, a comparison theorem between relative de Rham cohomology and Dwork cohomology is established in a paper by Dimca-Maaref-Sabbah-S…