Related papers: Specialization of integral dependence for modules

We introduce the module of derivations $\Theta_{h,M}$ attached to a given analytic map $h:(\mathbb C^n,0)\to (\mathbb C^p,0)$ and a submodule $M\subseteq \mathcal O_n^p$ and analyse several exact sequences related to $\Theta_{h,M}$.…

For the affine Lie algebra $C_2^{(1)}$ we study non-principal and non-coprincipal admissible modules of integer level and their quantum Hamiltonian reduction, and show that they have $\Gamma_0(2)$-modular invariance.

Let $B$ be a finite dimensional algebra and $A=B[P_0]$ be the one-point extension algebra of $B$ with respect to the finitely generated projective $B$-module $P_0$. The categories of $B$-modules and $A$-modules are related by two adjoint…

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…

Let (X_R, 0) be a germ of real analytic subset in (R^N, 0) of pure dimension n+1 with an isolated singularity at 0. Let (f_R,0) : (X_R, 0) --> (R,0) a real analytic germ with an isolated singularity at 0, such that its complexification f_C…

We introduce a notion of strong periodicity of a module over a finite-dimensional algebra over a field. We prove that the existence of such modules over certain idempotent algebras is both a necessary and sufficient condition for the…

We define spreadability systems as a generalization of exchangeability systems in order to unify various notions of independence and cumulants known in noncommutative probability. In particular, our theory covers monotone independence and…

Boij-S\"oderberg theory characterizes syzygies of graded modules and sheaves on projective space. This paper continues earlier work with S. Sam, extending the theory to the setting of $GL_k$-equivariant modules and sheaves on Grassmannians.…

We introduce the restricted local volume of a relatively very ample invertible sheaf as an invariant of equisingularity by determining its change across families. We apply this result to give numerical control of Whitney-Thom (differential)…

Given an isolated, quasi-homogeneous singularity $X$ we prove that there is a group isomorphism between the group of rank one reflexive sheaves on $X$ and the free abelian group generated by $\mathbb{C}^*$-divisors, modulo linear…

Let f be a hypersurface surface local singularity whose zero set has 1-dimensional singular locus. We develop an explicit procedure that provides the boundary of the Milnor fibre of f as an oriented plumbed 3-manifold. The method provides…

We study the behaviour of the finiteness of the set of associated primes of local cohomology modules, more generally of Lyubeznik functors, under various ring extensions. At first, we review the results for flat and faithfully flat…

Let G be a simple, simply connected algebraic group defined over an algebraically closed field k of positive characteristic p. Let \sigma:G->G be a strict endomorphism (i. e., the subgroup G(\sigma) of \sigma-fixed points is finite). Also,…

We revisit the concept of a minimal basis through the lens of the theory of modules over a commutative ring $R$. We first review the conditions for the existence of a basis for submodules of $R^n$ where $R$ is a B\'{e}zout domain. Then, we…

In this work, we consider a finitely determined map germ $f$ from $(\mathbb{C}^2,0)$ to $(\mathbb{C}^3,0)$. We characterize the Whitney equisingularity of an unfolding $F=(f_t,t)$ of $f$ through the constancy of a single invariant in the…

We study irreducible restrictions from modules over alternating groups to subgroups. We get reduction results which substantially restrict the classes of subgroups and modules for which this is possible. This is known when the…

Describing the decomposition of Foulkes module $F_b^a$ into irreducible Specht modules is an open problem for $a,b > 3$. In this article we provide a new approach for the Generalized Foulkes module $F_{\nu}^a$ (with arbitrary partition…

We establish the higher fractional differentiability for the minimizers of non-autonomous integral functionals of the form \begin{equation} \mathcal{F}(u,\Omega):=\int_\Omega \left[ f(x,Du)- g \cdot u \right] dx , \notag \end{equation}…

We study closedness of the range, adjointability and generalized invertibility of modular operators between Hilbert modules over locally C*-algebras of coefficients. Our investigations and the recent results of M. Frank [Characterizing…

We define the abelian fundamental group with modulus of a regular flat scheme over a discrete valuation ring, taking into account wild ramification along a divisor. Our definition provides a mixed-characteristic analogue of the abelian…