Related papers: Pull-back and push-forward functors for holonomic …
The two main theorems proved here are as follows: If $A$ is a finite dimensional algebra over an algebraically closed field, the identity component of the algebraic group of outer automorphisms of $A$ is invariant under derived equivalence.…
In this paper, we shall consider the notion of hyperbolic semi norm which on a module $X$ to set of all positive hyperbolic numbers. We shall prove the characterization of continuity of hyperbolic semi norm in this setup. We shall prove…
We give sufficient conditions for homotopical localization functors to preserve algebras over coloured operads in monoidal model categories. Our approach encompasses a number of previous results about preservation of structures under…
The irreducible alternative superbimodules are studied. The complete classification is obtained for even bimodules of arbitrary dimension and for finite-dimensional irreducible superbimodules over an algebraically closed field.
A holomorphic curve in moduli spaces is the image of a non-constant holomorphic map from a hyperbolic surface $B$ of type $(g,n)$ to the moduli space $\mathcal{M}_h$ of closed Riemann surfaces of genus $h$. We show that, when all peripheral…
We study the classification of submodules of module categories over monoidal categories, extending ideas of Coulembier on the classification of tensor ideals in monoidal categories. We develop a framework that applies to module categories…
We study moduli of semistable twisted sheaves on smooth proper morphisms of algebraic spaces. In the case of a relative curve or surface, we prove results on the structure of these spaces. For curves, they are essentially isomorphic to…
The main result of the paper establishes the irreducibility of a large family of nonzero central charge induced modules over Affine Lie algebras for any non standard parabolic subalgebra. It generalizes all previously known partial results…
Rigid monoidal 1-categories are ubiquitous throughout quantum algebra and low-dimensional topology. We study a generalization of this notion, namely rigid algebras in an arbitrary monoidal 2-category. Examples of rigid algebras include…
We show that compact subanalytic stratified spaces and algebraic stratifications of real varieties have finite exit-path $\infty$-categories, refining classical theorems of Lefschetz-Whitehead, Lojasiewicz, and Hironaka on the finiteness of…
The rational Cherednik algebra $\HH$ is a certain algebra of differential-reflection operators attached to a complex reflection group $W$. Each irreducible representation $S^\lambda$ of $W$ corresponds to a standard module $M(\lambda)$ for…
In this article, we study criteria for producing six-functor formalisms and morphisms between them. One notable application is that the motivic homotopy theory of algebraic stacks is the universal six-functor functor formalism in a strong…
The sheaf-function correspondence identifies the group of constructible functions on a real analytic manifold $M$ with the Grothendieck group of constructible sheaves on $M$. When $M$ is a finite dimensional real vector space,…
We extend the category of (super)manifolds and their smooth mappings by introducing a notion of microformal or "thick" morphisms. They are formal canonical relations of a special form, constructed with the help of formal power expansions in…
We study groups of germs of complex diffeomorphisms having a property called irreducibility. The notion is motivated by a similar property of the fundamental group of the complement of an irreducible hypersurface in the complex projective…
We take a unifying and new approach toward polynomial and trigonometric approximation in an arbitrary number of variables, resulting in a precise and general ready-to-use tool that anyone can easily apply in new situations of interest. The…
We revisit sheaves on locales by placing them in the context of the theory of quantale modules. The local homeomorphisms $p:X\to B$ are identified with the Hilbert $B$-modules that are equipped with a natural notion of basis. The…
Let $D, \Omega_1, ..., \Omega_m$ be irreducible bounded symmetric domains. We study local holomorphic maps from $D$ into $\Omega_1 \times... \Omega_m$ preserving the invariant $(p, p)$-forms induced from the normalized Bergman metrics up to…
We bring spaces over the classifying space $BS^1$ of the circle group $S^1$ to persistence theory via the singular cohomology with coefficients in a field. Then, the {\it cohomology} interleaving distance (CohID) between spaces over $BS^1$…
We propose a new model of ergodic optimization for expansive dynamical systems: the holonomic setting. In fact, we introduce an extension of the standard model used in this theory. The formulation we consider here is quite natural if one…