Related papers: $\mu hom$ and multi-microlocal operators

We make a first step towards categorification of the dendriform operad, using categories of modules over the Tamari lattices. This means that we describe some functors that correspond to part of the operad structure.

Suppose we are given complex manifolds $X$ and $Y$ together with substacks $\mathcal{S}$ and $\mathcal{S}'$ of modules over algebras of formal deformation $\mathcal{A}$ on $X$ and $\mathcal{A}'$ on $Y$, respectively. Suppose also we are…

In this paper we construct a large class of multiplication operators on reproducing kernel Hilbert spaces which are {\em homogeneous} with respect to the action of the M\"{o}bius group consisting of bi-holomorphic automorphisms of the unit…

We show the compatibility between the moderate or nearby cycle functor for regular holonomic $\mathcal{D}$-modules, as defined by Beilinson, Kashiwara and Malgrange, and the Hermitian duality functor, as defined by Kashiwara.

The present article deals with properties of one class of functions with complicated local structure. These functions can be modeled by certain operators of digits. Such operators were considered by the author earlier (for example, see [27,…

Let $k$ be a commutative $\mathbb{Q}$-algebra. We study families of functors between categories of finitely generated $R$-modules which are defined for all commutative $k$-algebras $R$ simultaneously and are compatible with base changes.…

In this paper, we consider the locally convex spaces of entire functions with growth given by proximate orders, and study the representation as a differential operator of a continuous homomorphism from such a space to another one. As a…

We survey divisibility properties of the Fourier coefficients of modular functions inspired by Ramanujan. Then using recent results of the generalized Hecke operator on harmonic Maass functions and known divisibility of Fourier coefficients…

In this paper we show that the Baues-Wirsching complex used to define cohomology of categories is a 2-functor from a certain 2-category of natural systems of abelian groups to the 2-category of chain complexes, chain homomorphism and…

Simplicial presheaves on cartesian spaces provide a general notion of smooth spaces. There is a corresponding smooth version of the singular complex functor, which maps smooth spaces to simplicial sets. We consider the localisation of the…

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…

We define the notion of a trace kernel on a manifold M. Roughly speaking, it is a sheaf on M x M for which the formalism of Hochschild homology applies. We associate a microlocal Euler class to such a kernel, a cohomology class with values…

In this paper we further investigate the geometry of monads of order-preserving functionals and of positively homogeneous functionals. We prove that for any compactum X with $w(X) = \tau$ the map $\mu_F X$, where $F\in\{O,OH\}$, is…

We investigate Cohen factorizations of local ring homomorphisms from three perspectives. First, we prove a "weak functoriality" result for Cohen factorizations: certain morphisms of local ring homomorphisms induce morphisms of Cohen…

The purpose of this paper is extend the notion of morphism of groupoids introduced by Zakrzewski to locally compact $\sigma$-compact groupoids endowed with Haar systems and to use the extension to construct a covariant functor from this…

We introduce an exact functor defined on multigraded modules which we call the expansion functor and study its homological properties. The expansion functor applied to a monomial ideal amounts to substitute the variables by monomial prime…

The Hom closed colocalizing subcategories of the stable module category of a finite group are classified. Along the way, the colocalizing subcategories of the homotopy category of injectives over an exterior algebra, and the derived…

Let $M$ be a compact torsion-free $G_2$ 7-manifold or Calabi-Yau 6-manifold. We prove Hodge decomposition theorems for the $dd^\phi$ operators, introduced by Harvey and Lawson, which generalize the $i\partial\bar\partial$ operator used in…

In this paper, we continue studying the properties of $\gamma$-semi-continuous and $\gamma$-semi-open functions introduced in [5].

Homotopical localizations with respect to a set of maps are known to exist in cofibrantly generated model categories (satisfying additional assumptions). In this paper we expand the existing framework, so that it will apply to not…