# Constructibility of tempered solutions of holonomic D-modules

@article{Morando2010ConstructibilityOT, title={Constructibility of tempered solutions of holonomic D-modules}, author={Giovanni Morando}, journal={arXiv: Algebraic Geometry}, year={2010} }

In this paper we prove the preconstructibility of the complex of tempered holomorphic solutions of holonomic D-modules on complex analytic manifolds. This implies the finiteness of such complex on any relatively compact open subanalytic subset of a complex analytic manifold. Such a result is an essential step for proving a conjecture of M. Kashiwara and P. Schapira (2003) on the constructibility of such complex.

## 6 Citations

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## References

SHOWING 1-10 OF 38 REFERENCES

An Existence Theorem for Tempered Solutions of D-Modules on Complex Curves

- Mathematics
- 2006

Let X be a complex curve, Xsa the subanalytic site associated to X, M a holonomic DX -module. Let Ot Xsa be the sheaf on Xsa of tempered holomorphic functions and S ol(M) (resp. S olt(M)) the complex…

On a reconstruction theorem for holonomic systems

- Mathematics
- 2012

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. Denote by t the affine…

Periods for flat algebraic connections

- Mathematics
- 2009

In previous work (Hien, Math. Ann. 337, 631–669, 2007), we established a duality between the algebraic de Rham cohomology of a flat algebraic connection on a smooth quasi-projective surface over the…

Tempered solutions of $\mathcal D$-modules on complex curves and formal invariants

- Mathematics
- 2007

Let $X$ be a complex analytic curve. In this paper we prove that the subanalytic sheaf of tempered holomorphic solutions of $\mathcal D_X$-modules induces a fully faithful functor on a subcategory of…

Microlocalization of Subanalytic Sheaves

- Mathematics
- 2007

Abstract In this Note we define specialization and microlocalization for sheaves on the subanalytic site. Applying these functors to the sheaves of tempered and Whitney holomorphic functions we get a…

Periods for irregular singular connections on surfaces

- Mathematics
- 2006

Given an integrable connection on a smooth quasi-projective algebraic surface U over a subfield k of the complex numbers, we define rapid decay homology groups with respect to the associated analytic…

On the Maximally Overdetermined System of Linear Differential Equations (I) (超函数と線型微分方程式 II)

- Mathematics
- 1974

The purpose of this paper is to present finiteness theorems and several properties of cohomologies of holomorphic solution sheaves of maximally overdetermined systems of linear differential…

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…

Good formal structure for meromorphic flat connections on smooth projective surfaces

- Mathematics
- 2008

We prove the algebraic version of a conjecture of C. Sabbah on the existence of the good formal structure for meromorphic flat connections on surfaces after some blow up.