Related papers: Nagata compactification for algebraic spaces

Every topological group $G$ has some natural compactifications which can be a useful tool of studying $G$. We discuss the following constructions: (1) the greatest ambit $S(G)$ is the compactification corresponding to the algebra of all…

We prove that a standard realization of the direct image complex via the so-called Douady-Barlet morphism associated with a smooth complex analytic surface admits a natural decomposition in the form of an injective quasi-isomorphism of…

In this article, we prove a Reocurrence Theorem over function fields of curves over $\mathbf{C}(\! (t)\! )$ and over finite extensions of the Laurent series field $\mathbf{C}(\! (x,y)\! )$. This provides a partial replacement to…

By making use of the classification of real simple Lie algebra, we get the maximum of the squared length of restricted roots case by case, thus we get the upper bounds of sectional curvature for irreducible Riemannian symmetric spaces of…

We prove that all spaces of finite Assouad-Nagata dimension admit a good order for Travelling Salesman Problem, and provide sufficient conditions under which the converse is true. We formulate a conjectural characterisation of spaces of…

We generalize all known results on rigidity of uniform Roe algebras to the setting of arbitrary uniformly locally finite coarse spaces. For instance, we show that isomorphism between uniform Roe algebras of uniformly locally finite coarse…

It is a longstanding problem whether every contractible Banach algebra is necessarily finite-dimensional. In this note, we confirm this for Banach algebras acting on Banach spaces with the uniform approximation property. This generalizes a…

A classical result of Fekete gives necessary conditions on a compact set in the complex plane so that it contains infinitely many sets of conjugate algebraic integers. For such sets, we demonstrate the existence of a sequence of algebraic…

Let G be a connected semisimple group over a non-Archimedean local field. For every faithful, geometrically irreducible linear representation of G we define a compactification of the associated Bruhat-Tits building X(G). This yields a…

This work addresses certain ambiguities in the Dirac approach to constrained systems. Specifically, we investigate the space of so-called ``rigging maps'' associated with Refined Algebraic Quantization, a particular realization of the Dirac…

It is known that locally compact groups approximable by finite ones are unimodular, but this condition is not sufficient, for example, the simple Lie groups are not approximable by finite ones as topological groups. In this paper the…

We study geometric and topological properties of infinite graphs that are quasi-isometric to a planar graph of bounded degree. We prove that every locally finite quasi-transitive graph excluding a minor is quasi-isometric to a planar graph…

We explore the possibility of extending Mardare et al. quantitative algebras to the structures which naturally emerge from Combinatory Logic and the lambda-calculus. First of all, we show that the framework is indeed applicable to those…

We consider the problem of extending maps from algebras to their profinite completions in finitely generated quasivarieties. Our developments are based on the construction of the profinite completion of an algebra as its natural extension.…

This paper generalizes the fundamental GAGA results of Serre cite{MR0082175} in three ways---to the non-separated setting, to stacks, and to families. As an application of these results, we show that analytic compactifications of…

Resolving a conjecture of von Neumann, Ogata's theorem in arXiv:1111.5933 showed the highly nontrivial result that arbitrarily many matrices corresponding to macroscopic observables with $N$ sites and a fixed site dimension $d$ are…

The algebraic method of singular reduction is applied for non regular group action on manifolds which provides singular symplectic spaces. The problem of deformation quantization of the singular surfaces is the focus. For some examples of…

A complete p-adic Khintchine type theorem for approximation by p-adic algebraic numbers is established.

We study extensions and generalizations of the Schmidt Subspace Theorem in various settings. In particular, we prove results for algebraic points of bounded degree, giving a sharp version of Schmidt's theorem for quadratic points in the…

In this paper we develop the compactness theorem for $\lambda$-surface in $\mathbb R^3$ with uniform $\lambda$, genus, and area growth. This theorem can be viewed as a generalization of Colding-Minicozzi's compactness theorem for…