Related papers: Localization, Local--Global Transfer, and Hull The…

In this article we show how one can use the local models of integrable Hamiltonian systems near critical points to prove a localization theorem for certain singular loci of integrables semi-toric systems for dimension greater than 4.

We consider matrices with entries in a local ring, Mat(R). Fix a group action, G on Mat(R), and a subset of allowed deformations, \Sigma. The traditional objects of study in Singularity Theory and Algebraic Geometry are the tangent spaces…

Stone locales together with continuous maps form a coreflective subcategory of spectral locales and perfect maps. A proof in the internal language of an elementary topos was previously given by the second-named author. This proof can be…

Let $X \overset{f}\longrightarrow S$ be a morphism of Noetherian schemes, with $S$ reduced. For any closed subscheme $Z$ of $X$ finite over $S$, let $j$ denote the open immersion $X\setminus Z \hookrightarrow X$. Koll\'ar asked whether for…

The aim of this note is to prove an analog of the flattening decomposition theorem for reflexive hulls. The main applications are: the construction of the moduli space of varieties of general type, improved flatness conditions and criteria…

This paper aims at developing a "local--global" approach for various types of finite dimensional algebras, especially those related to Hecke algebras. The eventual intention is to apply the methods and applications developed here to the…

We present various approaches to J. Herzog's theory of generalized local cohomology and explore its main aspects, e.g., (non-)vanishing results as well as a general local duality theorem which extends, to a much broader class of rings,…

The noncommutative (Cohn) localization S^{-1}R of a ring R is defined for any collection S of morphisms of f.g. projective left R-modules. We exhibit S^{-1}R as the endomorphism ring of R in an appropriate triangulated category. We use this…

In this article a higher order support theory, called the cohomological jump loci, is introduced and studied for dg modules over a Koszul extension of a local dg algebra. The generality of this setting applies to dg modules over local…

The local trajectories method establishes invertibility in algebras $\mathcal{B}= \alg(\mathcal{A}, U_G)$, for a unital $C^*$-algebra $\mathcal{A}$ with a non-trivial center, and a unitary group $U_g$, $g\in G$, with $G$ a discrete group,…

Given a $D$-module $M$ generated by a single element, and a polynomial $f$, one can construct several $D$-modules attached to $M$ and $f$ and can define the notion of the (generalized) $b$-function following M. Kashiwara. These modules are…

The product formula, commonly known as Trotter decomposition, is a central tool for digital quantum simulation, whose performance depends critically on how the Hamiltonian is partitioned into tractable blocks. Standard decompositions…

We define the localisation of a Hilbert module in analogy to the local multiplier algebra. We use properties of this localisation to enrich non-closed actions on $C^*$-algebras to closed actions on local multiplier algebras, and descend…

Let $R$ be a commutative Noetherian ring, $\fa$ an ideal of $R$, $M$ an arbitrary $R$-module and $N$ a finite $R$-module. We prove that \cite[Theorem 2.1]{Mel} and \cite[Proposition 3.3 (i)$\Leftrightarrow$(ii)]{B1} are true for any Serre…

In this paper we propose a general functorial definition of the operation of \emph{local tropicalization} in commutative algebra. Let $R$ be a commutative ring, $\Gamma$ a finitely generated subsemigroup of a lattice, $\gamma : \Gamma…

The main content of this treatise is a new concept in nonperturbative non-Lagrangian QFT which explains and extends the ad hoc constructions in low-dimensional models and incorporates them together with the higher dimensional theories into…

For a finite ring $R$, not necessarily commutative, we prove that the category of $\text{VIC}(R)$-modules over a left Noetherian ring $\mathbf{k}$ is locally Noetherian, generalizing a theorem of the authors that dealt with commutative $R$.…

We study the structure of an idempotent matrix $F$ over a commutative ring. We make explicit the fundamental system of orthogonal idempotents, hidden in this matrix, for each of which the matrix has a well-defined rank. Similarly we find a…

Normal elements (or multipliers) of the C* algebra of a certain class of locally compact groupoids admit a natural faithful representation as normal operators on the $L^2$-space of a dense orbit of the groupoid. We prove norm estimates on…

In arXiv:2511.04191 we constructed schemes of objects in small categories which contained a set of basepoints with local representing (localizing) objects. Here we prove that the category $\cat{Rings}$ of associative rings with unit has a…