Related papers: Universal ringed spaces
Faithful representations of regular $\ast$-rings and modular complemented lattices with involution within orthosymmetric sesquilinear spaces are studied within the framework of Universal Algebra. In particular, the correspondence between…
Finite metric spaces arise in many different contexts. Enormous bodies of data, scientific, commercial and others can often be viewed as large metric spaces. It turns out that the metric of graphs reveals a lot of interesting information.…
We calculate a projective space of essential measured laminations in a surface pair, which will be used in another paper to help describe spaces of "finite height laminations."
We consider the space of embeddings of finitely many circles that bound disks in non-positively curved surfaces. We index the connected components of this space with finite rooted trees and show that the connected components are classifying…
We describe a number of geometric contexts where categorification appears naturally: coherent sheaves, constructible sheaves and sheaves of modules over quantizations. In each case, we discuss how "index formulas" allow us to easily perform…
A recent paper showed how to find sets of finite affine or projective planes constructed on a common set of points, so that lines of one plane meet lines of a different plane in at most two points. In this paper, those results are…
We study the projections in vector spaces over finite fields. We prove finite fields analogues of the bounds on the dimensions of the exceptional sets for Euclidean projection mapping. We provide examples which do not have exceptional…
Finite projective (lattice) geometries defined over rings instead of fields have recently been recognized to be of great importance for quantum information theory. We believe that there is much more potential hidden in these geometries to…
We describe all affine maps from a Riemannian manifold to a metric space and all possible image spaces.
We formulate a notion of "geometric reductivity" in an abstract categorical setting which we refer to as adequacy. The main theorem states that the adequacy condition implies that the ring of invariants is finitely generated. This result…
For any finite totally ordered set, the multisets of intervals form an abelian category. Various classes of subcategories admit natural combinatorial descriptions, and counting them yields familiar integer sequences. Surprisingly, in some…
We investigate braid group representations associated with unitary braided vector spaces, focusing on a conjecture that such representations should have virtually abelian images in general and finite image provided the braiding has finite…
We describe the integral equivariant cohomology ring of a weighted projective space in terms of piecewise polynomials, and thence by generators and relations. We deduce that the ring is a perfect invariant, and prove a Chern class formula…
The $H$-ring structure of certain infinite(-dimensional) Grassmannians is discussed using various algebraic and analytical methods but so that cellular arguments are avoided. These methods allow us to discuss these Grassmannian in greater…
We prove that direct limits of finite dimensional Lie algebroids and their prolongations can be endowed with structures of convenient spaces.
It is shown that any finitely generated subring of a global field has a universal first-order definition in its fraction field. This covers Koenigsmann's result for the ring of integers and its subsequent extensions to rings of integers in…
The notion of symmetry in polynomial rings with several indeterminates is generalized to polynomial rings over finite fields. Families of extensions of the projective line over a finite field of constants possessing this property are…
Inspired by the perspective of Reyes' noncomutative spectral theory, we attempt to develop noncommutative algebraic geometry by introducing ringed coalgebras, which can be thought of as a noncommutative generalization of schemes over a…
We consider groups $\mathbb{I}$ of isometries of ultrametric Urysohn spaces $\mathbb{U}$. Such spaces $\mathbb{U}$ admit transparent realizations as boundaries of certain $R$-trees and the groups $\mathbb{I}$ are groups of automorphisms of…
We investigate the local properties of Berkovich spaces over Z. Using Weierstrass theorems, we prove that the local rings of those spaces are noetherian, regular in the case of affine spaces and excellent. We also show that the structure…