Related papers: Galois connections between closure spaces

We give a detailed proof of Kolchin's results on differential Galois groups of strongly normal extensions, in the case where the field of constants is not necessarily algebraically closed. We closely follow former works due to Pillay and…

We introduce the new notion of the "quasi-Galois point" in Algebraic geometry, which is a generalization of the Galois point. A point $P$ in projective plane is said to be quasi-Galois for a plane curve if the curve admits a non-trivial…

Over a global field (number field or function field of a curve over a finite field), theorems for the Galois cohomology of algebraic groups have long been known. For $F$ the function field of a curve over the formal series field…

In this paper we define operations of preradicals of any abelian category. We define idempotent preradicals and radicals. We prove that every adjoint pair between abelian categories induces a Galois connection between the corresponding…

Given a family of continuous real functions $\mathcal{G}$, let $R_\mathcal{G}$ be a binary relation defined as follows: a continuous function $f\colon\mathbb{R}\to\mathbb{R}$ is in the relation with a closed set $E\subseteq\mathbb{R}$ if…

We give a topological interpretation of the space of $L^2$ harmonis forms of some QALE manifolds introduced by D. Joyce. We introduce a analytical criterium which make possible the used of Mayer-Vietoris sequence.

We prove that the non-ordinary component is connected in the moduli spaces of finite flat models of two-dimensional local Galois representations over finite fields. This was conjectured by Kisin. As an application to global Galois…

We introduce the concept of a Galois covering of a pointed coalgebra. The theory developed shows that Galois coverings of pointed coalgebras can be concretely expressed by smash coproducts using the coaction of the automorphism group of the…

In this paper the transcendental Galois extensions of a field will be introduced as counterparts to algebraic Galois ones. There exist several types of transcendental Galois extensions of a given field, from the weakest one to the strongest…

This paper introduces and develops M\"obius homology, a homology theory for representations of finite posets into abelian categories. Although the connection between poset topology and M\"obius functions is classical, we go further by…

We prove that a certain class of open homomorphisms between Galois groups of function fields of curves over finite fields arise from embeddings between the function fields.

The classification of G-spaces by Palais is refined for the case where the orbit space satisfies certain mild topological hypotheses. It is shown that when a sequence of such orbit spaces is "close" to a limit orbit space, in some suitable…

Let $\rho_1$ and $\rho_2$ be a pair of residual, odd, absolutely irreducible two-dimensional Galois representations of a totally real number field $F$. In this article we propose a conjecture asserting existence of "safe" chains of…

The aim of this article is to study rational parallelisms of algebraic varieties by means of the transcendence of their symmetries. The nature of this transcendence is measured by a Galois group built from the Picard-Vessiot theory of…

We define Galois coverings on tropical curves for which a Galois correspondence and a universal mapping property hold.

The notion of preopen sets and precontinuity in a topological space was introduced by Mashhour et. al in 1982 [13]. Later the same was studied in a bitopological space in [7] and [9]. Here we have studied the idea of pairwise preopen sets…

We introduce the notion of Galois holomorphic foliation on the complex projective space as that of foliations whose Gauss map is a Galois covering when restricted to an appropriate Zariski open subset. First, we establish general criteria…

We revisit the problem of Stone duality for lattices with various quasioperators, first studied in [14], presenting a fresh duality result. The new result is an improvement over that of [14] in two important respects. First, the…

We compute the Galois groups for a certain class of polynomials over the the field of rational numbers that was introduced by S. Mori and study the monodromy of corresponding hyperelliptic jacobians.

We present a shortcut to the familiar characterizations of finite Galois extensions, based on an idea from an earlier Monthly note by Sonn and Zassenhaus.