Related papers: Covering groupoids
We give an overview of differential cohomology from the point of view of algebraic topology. This includes a survey of several different definitions of differential cohomology groups, a discussion of differential characteristic classes, an…
On objects of a triangulated category with a stability condition, we construct a topology.
Let G be a finite group and \rho: G--> End(E) be a group representation of G on a coherent sheaf over an integral scheme. The purpose of this paper shall give a decomposition theorem of such representations in non-splitting components and…
In this paper we will give the calculus, the criterion, and the existence of the arithmetic Galois covers of higher relative dimensions.
In this work, we prove that if a triangular algebra $A$ admits a strongly simply connected universal Galois covering for a given presentation then the fundamental group associated to this presentation is free.
We introduce some compact orbifolds on which there is a certain finite group action having a simple convex polytope as the orbit space. We compute the orbifold fundamental group and homology groups of these orbifolds. We calculate the…
Topological groupoids admit various types of morphisms. We push these notions to the level of continuous groupoid actions to obtain various types of groupoid action morphisms. Some dynamical properties and their relation to these morphisms…
We give a short proof that, for nice $X$, the based fundamental groupoid of $X$ with topology induced by the compact open topology on the space of paths, is indeed the universal covering space of $X$.
Motivated by Quantum Mechanics considerations, we expose some cross product constructions on a groupoid structure. Furthermore, critical remarks are made on some basic formal aspects of the Hopf algebra structure.
We give a notion of a comatrix coring which embodies all former constructions and, what is more interesting, leads to the formulation of a notion of Galois coring and the statement of a Faithfully Flat Descent Theorem that generalize the…
We explore the canonical Grothendieck topology in some specific circumstances. First we use a description of the canonical topology to get a variant of Giraud's Theorem. Then we explore the canonical Grothendieck topology on the categories…
This note is a development of our two previous papers, arXiv:1212.3392v1 and 1306.3660v1. The fundamental question is whether there exists a Galois theory, in which the Galois group is a quantum group. For a linear equations with respect to…
Characteristic properties of corings with a grouplike element are analysed. Associated differential graded rings are studied. A correspondence between categories of comodules and flat connections is established. A generalisation of the…
We prove an analog of the classical Hartogs extension theorem for certain (possibly unbounded) domains on coverings of Stein manifolds.
In this article we investigate the algebra and geometry of dihedral covers of smooth algebraic varieties. To this aim we first describe the Weil divisors and the Picard group of divisorial sheaves on normal double covers. Then we provide a…
The automorphism group of the Galois covering induced by a pluri-canonical generic covering of a projective space is investigated. It is shown that by means of such coverings one obtains, in dimensions one and two, serieses of specific…
This very speculative sketch suggests that a theory of fundamental groupoids for tensor triangulated categories could be used to describe the ring of integers as the singular fiber in a family of ring-spectra parametrized by a structure…
We suggest a generalization of \pi_0 for topological groupoids, which encodes incidence relations among the strata of the associated quotient object, and argue for its utility by example, starting from the orbit categories of the theory of…
We examine conditions under which there exists a non-constant family of Galois branched covers of curves over an algebraically closed field $k$ of fixed degree and fixed ramification locus, under a notion of equivalence derived from…
We give a group-theoretic description of the parity of a pull-back of a theta characteristic under a branched covering. It involves lifting monodromy of the covering to the semidirect product of the symmetric and Clifford groups, known as…