Related papers: On covering theory and its applications
This overview paper reviews several results relating the representation theory of quivers to algebraic geometry and quantum group theory. (Potential) applications to the study of the representation theory of wild quivers are discussed. To…
AF-rings are algebras over a field k which satisfy the Altitude Formula over k. This paper surveys a few works in the literature on the Krull and valuative dimensions of tensor products of AF-rings. The first section extends Wadsworth's…
We define covering and separation numbers for functions. We investigate their properties, and show that for some classes of functions there is exact equality of separation and covering. We provide analogues for various geometric…
This thesis develops some of the basic model theory of covers of algebraic curves. In particular, an equivalence between the good model-theoretic behaviour of the modular j-function, and the openness of certain Galois representations in the…
The aim of this article is to introduce Vogel's localization theorem for classes of D-complexes: this generalization of Waldhausen's localization theorem is especially useful and powerful in that it gives an explicit and computable…
The study of the packing of a length of wire in a two dimensional domain is done using techniques of conformal maps. The resulting scaling properties are derived through the Coulomb gas formalism of Conformal Field Theories. An analogy is…
In math.RT/0302174 we developed a framework to study representations of groups of the form $G((t))$, where $G$ is an algebraic group over a local field $K$. The main feature of this theory is that natural representations of groups of this…
Koszul duality and covering theory are combined to realise the bounded derived category D of an algebra with radical square zero as a certain orbit category of the bounded derived category of finitely presented representations of an…
We develop some algebraic structure notions such as composition series and convexity degree, along with some notions holding a geometric interpretation, like reducibility and hyperdimension, with the main objective being a tropical…
Locally cartesian closed (lcc) categories are natural categorical models of extensional dependent type theory. This paper introduces the "gros" semantics in the category of lcc categories: Instead of constructing an interpretation in a…
We develop the notion of a geometric covering of a rigid space X, which yields a much larger class of covering spaces than that studied previously by de Jong. Geometric coverings of X are closed under disjoint unions and are \'etale local…
We describe a new construction of families of Galois coverings of the line using basic properties of configuration spaces, covering theory, and the Grauert-Remmert Extension Theorem. Our construction provides an alternative to a previous…
This article extends the study of cyclic ramified covers of the projective line defined by Kummer equations. We consider the most general case of such covers, allowing arbitrary orders in the roots of the generating radicant. The primary…
Let $G$ be a finitely presented group. A new complexity called \textit{Karoubi-Weibel complexity} or \textit{covering type}, is defined for $G$. The construction is inspired by recent work of Karoubi and Weibel \cite{KW}, initially applied…
We prove bounds for the covering numbers of classes of convex functions and convex sets in Euclidean space. Previous results require the underlying convex functions or sets to be uniformly bounded. We relax this assumption and replace it…
Braid groups are an important and flexible tool used in several areas of science, such as Knot Theory (Alexander's theorem), Mathematical Physics (Yang-Baxter's equation) and Algebraic Geometry (monodromy invariants). In this note we will…
In this Master of Science Thesis I introduce geometric algebra both from the traditional geometric setting of vector spaces, and also from a more combinatorial view which simplifies common relations and operations. This view enables us to…
These notes are based on a talk given at the Summer School "Infinite-dimensional representations of finite-dimensional algebras" held at the University of Manchester in September 2015. They intend to provide a brief introduction to the…
We prove a generalization of the fundamental theorem of algebraic K-theory for Verdier-localizing functors by extending the proof for algebraic K-theory of spaces to the realm of stable $\infty$-categories. The formula behaves much better…
We show that differential calculus (in its usual form, or in the general form of topological differential calculus) can be fully imdedded into a functor category (functors from a small category of anchord tangent algebras to anchored sets).…