ﻻ يوجد ملخص باللغة العربية
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 $mathcal{M}mapstomathcal{M}_{mathrm{reg}}$, called regularization. Recall that $mathcal{M}_{mathrm{reg}}$ is reconstructed from the de Rham complex of $mathcal{M}$ by the regular Riemann-Hilbert correspondence. Similarly, on a topological space, the embedding of sheaves into enhanced ind-sheaves has a left quasi-inverse functor, called here sheafification. Regularization and sheafification are intertwined by the irregular Riemann-Hilbert correspondence. Here, we study some of their properties. In particular, we provide a germ formula for the sheafification of enhanced specialization and microlocalization.
On a complex symplectic manifold we prove a finiteness result for the global sections of solutions of holonomic DQ-modules in two cases: (a) by assuming that there exists a Poisson compactification (b) in the algebraic case. This extends our previous
For a smooth variety $Y$ over a perfect field of positive characteristic, the sheaf $D_Y$ of crystalline differential operators on $Y$ (also called the sheaf of $PD$-differential operators) is known to be an Azumaya algebra over $T^*_{Y},$ the cotang
We introduce a concept of a fractional-derivatives series and prove that any linear partial differential equation in two independent variables has a fractional-derivatives series solution with coefficients from a differentially closed field of zero c
The aim of this Note is to specify the links between the three kinds of Lisbon integrals, trace functions and trace forms with the corresponding D--modules.
Let $X$ be a complex analytic manifold, $Dsubset X$ a locally quasi-homogeneous free divisor, $E$ an integrable logarithmic connection with respect to $D$ and $L$ the local system of the horizontal sections of $E$ on $X-D$. In this paper we give an a