# Irregular perverse sheaves

@article{Kuwagaki2018IrregularPS, title={Irregular perverse sheaves}, author={Tatsuki Kuwagaki}, journal={Compositio Mathematica}, year={2018}, volume={157}, pages={573 - 624} }

We introduce irregular constructible sheaves, which are ${\mathbb {C}}$-constructible with coefficients in a finite version of the Novikov ring $\Lambda$ and special gradings. We show that the bounded derived category of cohomologically irregular constructible complexes is equivalent to the bounded derived category of holonomic ${\mathcal {D}}$-modules by a modification of D’Agnolo and Kashiwara's irregular Riemann–Hilbert correspondence. The bounded derived category of cohomologically…

## 8 Citations

### Note on algebraic irregular Riemann–Hilbert correspondence

- MathematicsRendiconti del Seminario Matematico della Università di Padova
- 2023

The subject of this paper is an algebraic version of the irregular Riemann-Hilbert correspondence which was mentioned in [arXiv:1910.09954] by the author. In particular, we prove an equivalence of…

### $\hbar$-Riemann-Hilbert correspondence

- Mathematics
- 2022

We formulate and prove a Riemann–Hilbert correspondence between ~-differential equations and sheaf quantizations, which can be considered as a correspondence between two kinds of quantizations…

### Categorification of Legendrian knots

- Mathematics
- 2019

Perverse schober defined by Kapranov--Schechtman is a categorification of the notion of perverse sheaf. In their definition, a key ingredient is certain purity property of perverse sheaves. In this…

### Another proof of the Riemann-Hilbert Correspondence for Regular Holonomic D-Modules

- Mathematics
- 2023

In this paper, we reprove the Riemann–Hilbert correspondence for regular holonomic D -modules of [Kas84] (see also [Meb84]) by using the irregular Riemann– Hilbert correspondence of [DK16]. Moreover,…

### An introduction to sheaf quantization

- Philosophy
- 2022

. The notion of sheaf quantization has many faces: an enhancement of the notion of constructible sheaves, the Betti counterpart of Fukaya–Floer theory, a topological realization of WKB-states in…

### Remarks on rigid irreducible meromorphic connections on the projective line

- Mathematics
- 2022

We illustrate the Arinkin-Deligne-Katz algorithm for rigid irreducible meromorphic bundles with connection on the projective line by giving motivicity consequences similar to those given by Katz for…

### Moderate Growth and Rapid Decay Nearby Cycles via Enhanced Ind-Sheaves

- Mathematics
- 2022

. For any holomorphic function f : X → C on a complex manifold X , we deﬁne and study moderate growth and rapid decay objects associated to an enhanced ind-sheaf on X . These will be sheaves on the…

### Sheaf quantization from exact WKB analysis

- Mathematics
- 2020

A sheaf quantization is a sheaf associated to a Lagrangian brane. By using the ideas of exact WKB analysis, spectral network, and scattering diagram, we sheaf-quantize spectral curves over the…

## References

SHOWING 1-10 OF 40 REFERENCES

### Enhanced perversities

- MathematicsJournal für die reine und angewandte Mathematik (Crelles Journal)
- 2019

On a complex manifold, the Riemann–Hilbert correspondence embeds the triangulated category of (not necessarily regular) holonomic {\mathcal{D}}-modules into the triangulated category of…

### Curve test for enhanced ind-sheaves and holonomic $D$-modules, I

- MathematicsAnnales scientifiques de l'École Normale Supérieure
- 2022

Recently, the Riemann-Hilbert correspondence was generalized in the context of general holonomic D-modules by A. D'Agnolo and M. Kashiwara. Namely, they proved that their enhanced de Rham functor…

### Riemann-Hilbert correspondence for holonomic D-modules

- Mathematics
- 2016

The classical Riemann-Hilbert correspondence establishes an equivalence between the triangulated category of regular holonomic D$\mathcal{D}$-modules and that of constructible sheaves.In this paper,…

### Microlocal branes are constructible sheaves

- Mathematics
- 2006

Let X be a compact real analytic manifold, and let T* X be its cotangent bundle. In a recent paper with Zaslow (J Am Math Soc 22:233–286, 2009), we showed that the dg category Shc(X) of constructible…

### Good formal structures for flat meromorphic connections, II: Excellent schemes

- Mathematics
- 2010

Given a flat meromorphic connection on an excellent scheme over a field of characteristic zero, we prove existence of good formal structures after blowing up; this extends a theorem of Mochizuki for…

### Regular and Irregular Holonomic D-Modules

- Mathematics
- 2016

D-module theory is essentially the algebraic study of systems of linear partial differential equations. This book, the first devoted specifically to holonomic D-modules, provides a unified treatment…

### D-Modules, Perverse Sheaves, and Representation Theory

- Mathematics
- 2007

D-Modules and Perverse Sheaves.- Preliminary Notions.- Coherent D-Modules.- Holonomic D-Modules.- Analytic D-Modules and the de Rham Functor.- Theory of Meromorphic Connections.- Regular Holonomic…

### Lagrangian intersection floer theory : anomaly and obstruction

- Mathematics
- 2009

Part I Introduction Review: Floer cohomology The $A_\infty$ algebra associated to a Lagrangian submanifold Homotopy equivalence of $A_\infty$ algebras Homotopy equivalence of $A_\infty$ bimodules…

### Wild Harmonic Bundles and Wild Pure Twistor D-modules

- Mathematics
- 2008

We study (i) asymptotic behaviour of wild harmonic bundles, (ii) the relation between semisimple meromorphic flat connections and wild harmonic bundles, (iii) the relation between wild harmonic…