Related papers: Tempered solutions of $\mathcal D$-modules on comp…

Let X be a complex curve, $X_{sa}$ the subanalytic site associated to X, M a holonomic $D_X$-module. Let $O^t$ be the sheaf on $X_{sa}$ of tempered holomorphic functions, Sol(M) (resp. $Sol^t$(M)) the complex of holomorphic (resp. tempered…

Let $f:X\to Y$ be a smooth morphism of complex analytic manifolds and let $F$ be an $\mathbb{R}$-constructible complex on $Y$. Let $\cal{M}$ be a coherent $\shd_X$-module. We prove that the microsupport of the solution complex of $\shm$ in…

In this paper we prove the constructibility on the subanalytic sites of the sheaves of tempered holomorphic solutions of holonomic D-modules on complex analytic manifolds. Such a result solves a conjecture of M. Kashiwara and P. Schapira…

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…

Let X be a smooth complex manifold. Let Sol denote the solution functor for D-modules on X. Traditionally, the fully-faithfulness of Riemann-Hilbert correspondance is proved by showing that if M_1 and M_2 are regular holonomic D_X modules,…

We construct a fully-faithful functor of $\infty$-categories from complexes of D-cap modules with Fr\'echet cohomology to quasi-coherent sheaves on an analytic stack. We prove various descent results for $\infty$-categories of D-cap modules…

For a complex manifold $X$ the ring of microdifferential operators $\E_X$ acts on the microlocalization $\mu hom(F,\O_X)$, for $F$ in the derived category of sheaves on $X$. Kashiwara, Schapira, Ivorra, Waschkies proved, as a byproduct of…

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 gives a fully faithfully embedding of the…

Let $\mathcal{V}$ be a mixed characteristic complete discrete valuation ring, $\mathcal{P}$ a separated smooth formal scheme over $\mathcal{V}$, $P$ its special fiber, $X$ a smooth closed subscheme of $P$, $T$ a divisor in $P$ such that…

On a smooth algebraic variety over $\mathbb{C}$, we build the tempered subanalytic and Stein tempered subanalytic sites. We construct the sheaf of holomorphic functions tempered at infinity over these sites and study their relations with…

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 $\mathcal{M}\mapsto\mathcal{M}_{\mathrm{reg}}$, called regularization. Recall that…

We compute formal invariants associated with the cohomology sheaves of the direct image of holonomic D-modules of exponential type. We also prove that every formal C[[t]]<\partial_t>-modules is isomorphic, after a ramification, to a germ of…

The aim of this paper is to investigate the closed subschemes of moduli spaces corresponding to projective varieties which admit an effective action by a given finite group $G$. To achieve this, we introduce the moduli functor…

Let $X$ be a complex manifold. In "Microlocal study of Ind-sheaves I: microsupport and regularity", M. Kashiwara e P. Schapira made the conjecture that a holonomic D-module $\shm$ is regular holonomic if and only if…

A. D'Agnolo and M. Kashiwara proved that their enhanced solution functor induces a fully faithful embedding of the triangulated category of holonomic D-modules into the one of R-constructible enhanced ind-sheaves. In this paper, we define…

We study the truncated microsupport $Ss_k$ of sheaves on a real manifold. Applying our results to the case of $F=RHom_D(M,O)$, the complex of holomorphic solutions of a coherent $D$-module $M$, we show that $Ss_k(F)$ is completely…

A Lie algebroid on a variety X/k is an extension \alpha: g_X \to T_X of the tangent sheaf both as O_X-module and Lie algebra over the base field, with the obvious compatibilities; and given a Lie algebroid one has its associated ring of…

We describe the complex of solutions of the algebraic Mellin transform of a $\mathcal{D}$-module $\mathcal{M}$ in terms of the solutions of $\mathcal{M}$. In order to do that, we define a Mellin functor on sheaves. We show the Mellin…

We formalize, at the level of D-modules, the notion that A-hypergeometric systems are equivariant versions of the classical hypergeometric equations. For this purpose, we construct a functor on a suitable category of torus equivariant…

In this paper we define specialization and microlocalization for subanalytic sheaves. Applying these functors to the sheaves of tempered and Whytney holomorphic functions we get a unifying description of tempered and formal…