Related papers: Characteristic cycles associated to holonomic $\ma…

We undertake the study of bivariate Horn systems for generic parameters. We prove that these hypergeometric systems are holonomic, and we provide an explicit formula for their holonomic rank as well as bases of their spaces of complex…

This paper proves the existence of global rational structures on spaces of cusp forms of general reductive groups. We identify cases where the constructed rational structures are optimal, which includes the case of GL($n$). As an…

On the product of a complex manifold $X$ by a complex curve $S$ considered as a parameter space, we show a Riemann-Hilbert correspondence between regular holonomic relative $\mathcal D$-modules (resp. complexes) on the one hand and relative…

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…

Given a morphism $X \to S$ of log schemes of characteristic $p > 0$ and a lifting of $X'$ over $S$ modulo $p^2$, we use Lorenzon's indexed algebras $A_X^{gp}$ and $B_{X/S}$ to construct an equivalence between $O_X$-modules with nilpotent…

In this paper we study the comparison between the logarithmic and the meromorphic de Rham complexes along a divisor in a complex manifold. We focus on the case of free divisors, starting with the case of locally quasihomogeneous divisors,…

We generalize Rost's theory of cycle modules using Milnor-Witt K-theory instead of the classical Milnor K-theory. We obtain a (quadratic) setting to study general cycle complexes and their (co)homology groups. The usual constructions are…

Consider a complex symplectic manifold $X$ and the algebroid $W_X$ of quantization-deformation. For two regular holonomic modules $L_i$ ($i=0,1$) supported by smooth Lagrangian manifolds, we prove that the complex $Rhom_{W_X}(L_1,L_0)$ is…

Let $\mathfrak{X}$ be a formal smooth quasi-compact curve over a complete discrete valuation ring of mixed characteristic. We consider over $\mathfrak{X}$ the sheaves of differential operators $\widehat{\mathcal{D}}^{(0)}_{\mathfrak{X}, k ,…

A celebrated theorem of Harich-Chandra asserts that all invariant eigendistributions on a semisimple Lie group are locally integrable functions. We show that this result is a consequence of an algebraic property of a holonomic D-module…

We introduce the notion of a holonomic D-module on a smooth (idealized) logarithmic scheme and show that Verdier duality can be extended to this context. In contrast to the classical case, the pushforward of a holonomic module along an open…

For a polynomial ring $R=k[x_1,...,x_n]$, we present a method to compute the characteristic cycle of the localization $R_f$ for any nonzero polynomial $f\in R$ that avoids a direct computation of $R_f$ as a $D$-module. Based on this…

We define the notion of Betti structure for holonomic D-modules which are not necessarily regular singular. We establish the fundamental functorial properties. We also give auxiliary analysis of holomorphic functions of various types on the…

Let $M$ be a complex manifold, $D\subset M$ a free divisor and $U=M\setminus D$ its complement. In this paper we study the characteristic cycle $\textup{CC}(\gamma\cdot \ind_U)$ of the restriction of a constructible function $\gamma$ on…

Given a scheme in characteristic p together with a lifting modulo p^2, we construct a functor from a category of suitably nilpotent modules with connection to the category of Higgs modules. We use this functor to generalize the…

We propose two new approaches to the Tannakian Galois groups of holonomic D-modules on abelian varieties. The first is an interpretation in terms of principal bundles given by the Fourier-Mukai transform, which shows that they are almost…

We introduce the notion of a regular integrable connection on a smooth log scheme over $\mathbf{C}$ and construct an equivalence between the category of such connections and the category of integrable connections on its analytification,…

We formulate a general conjecture on the characteristic polynomials of S-decomposed T-ramified Iwasawa modules over the cyclotomic Z {\ell}-extension of a number field. We show that this conjecture is equivalent to the conjunctions of the…

We show the existence of and explicitly construct generic polynomials for various groups, over fields of positive characteristic. The methods we develop apply to a broad class of connected linear algebraic groups defined over finite fields…

We prove some sufficient conditions in order that a root of the Bernstein-Sato polynomial contributes to a difference between certain D-modules generated by rational powers of a holomorphic function; for instance, this holds in the case of…