Related papers: The local information of difference equations

Consider a subgroup of finite index of modular group. We give an analytic criterion for a cuspidal divisor to be torsion in the Jacobian of the corresponding modular curve. By BelyI theorem, such a criterion would apply to any curve over a…

We investigate the arithmetic of algebraic curves on coarse moduli spaces for special linear rank two local systems on surfaces with fixed boundary traces. We prove a structure theorem for morphisms from the affine line into the moduli…

Algebraic holonomic $\mathcal{D}$-modules on a complex line are classified by the associated topological data consisting of local systems with Stokes structure and the nearby and vanishing cycles at the singularities. The Fourier transform…

We introduce the notion of difference equation defined on a structured set. The symmetry group of the structure determines the set of difference operators. All main notions in the theory of difference equations are introduced as invariants…

Let G be a connected split reductive group over a complete discrete valuation ring of mixed characteristic. We use the theory of intermediate extensions due to Abe-Caro and arithmetic Beilinson-Bernstein localization to classify irreducible…

In this note, finite modules locally of finite injective dimension over commutative Noetherian rings are characterized in terms of vanishing of Ext modules.

In this paper, we investigate the local Euler obstruction and the relative local Euler obstruction in terms of constructible complexes of sheaves, characteristic cycles, and vanishing cycles. The fundamental tool that we use is the notion…

A new derivative, called deformable derivative, is introduced here which is equivalent to ordinary derivative in the sense that one implies other. The deformable derivative is defined using limit approach like that of ordinary one but with…

In this article we study the basic theoretical properties of Mellin-type fractional integrals, known as generalizations of the Hadamard-type fractional integrals. We give a new approach and version, specifying their semigroup property,…

Using approximations, we give several characterizations of separability of bimodules. We also discuss how separability properties can be used to transfer some representation theoretic properties from one ring to another one: contravariant…

The field of definition of an affine invariant submanifold M is the smallest subfield of the reals such that M can be defined in local period coordinates by linear equations with coefficients in this field. We show that the field of…

The matching distance is a pseudometric on multi-parameter persistence modules, defined in terms of the weighted bottleneck distance on the restriction of the modules to affine lines. It is known that this distance is stable in a reasonable…

Let A be a finitely generated associative algebra over an algebraically closed field. We characterize the finite dimensional modules over A whose orbit closures are regular varieties.

In D-module theory, we have the notion of the restriction of a module along a smooth variety. T. Oaku and N. Takayama have described a process to compute the restriction, which starts from a free resolution adapted to the V-filtration of…

Let $R$ be a commutative ring. Roughly speaking, we prove that an $R$-module $M$ is flat iff it is a direct limit of $R$-module affine algebraic varieties, and $M$ is a flat Mittag-Leffler module iff it is the union of its $R$-submodule…

We present a method to compute the holonomic extension of a $D$-module from a Zariski open set in affine space to the whole space. A particular application is the localization of coherent $D$-modules which are holonomic on the complement of…

This work studies limits of Pfaffian systems, a class of first-order PDEs appearing in the Feynman integral calculus. Such limits appear naturally in the context of scattering amplitudes when there is a separation of scale in a given set of…

We define the class of rigid Frobenius algebras in a (non-semisimple) modular category and prove that their categories of local modules are, again, modular. This generalizes previous work of A. Kirillov, Jr. and V. Ostrik [Adv. Math. 171…

We observe algebraic derivations on an affine domain B defined over an algebraically closed field of characteristic 0, which are called locally finite derivations in commutative and non-commutative contexts in other references. We observe…

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…