Related papers: Quasi-inverse endomorphisms

This article establishes the algebraic covering theory of quandles. For every connected quandle we explicitly construct a universal covering, which in turn leads us to define the algebraic fundamental group as the automorphism group of the…

A structure $\cal S$ is quasi-projective if for every structure $\cal T$, for every homomorphism $f : {\cal S} \rightarrow {\cal T}$ and every epimorphism $j: {\cal S}\rightarrow {\cal T}$ there is an endomorphism $\phi$ of $\cal S$ such…

For any finite group G and integer i, let $\mathcal{H}^i(G)$ be the set of all the isomorphism classes of the Galois cohomology groups $\hat{H}^i(K/k,E_K)$, where K/k runs over all the unramified G-extension of number fields and E_K denotes…

The l-adic parabolic cohomology groups attached to noncongruence subgroups of SL_2(Z) are finite-dimensional representations of Gal(Qbar/F) for some number field F. We exhibit examples (with F=Q) giving rise to Galois representations whose…

Let $L/K$ be a Galois extension of fields with Galois group $\Gamma$, and suppose $L/K$ is also an $H$-Hopf Galois extension. Using the recently uncovered connection between Hopf Galois structures and skew left braces, we introduce a method…

Let F be a global function field and let F^ab be its maximal abelian extension. Following an approach of D.Hayes, we shall construct a continuous homomorphism \rho: Gal(F^ab/F) \to C_F, where C_F is the idele class group of F. Using class…

In recent work, the authors proved a general result on lifting $G$-irreducible odd Galois representations $\mathrm{Gal}(\overline{F}/F) \to G(\overline{\mathbb{F}}_{\ell})$, with $F$ a totally real number field and $G$ a reductive group, to…

In previous joint work with Eli Aljadeff we attached a generic Hopf Galois extension A(H,c) to each twisted algebra H(c) obtained from a Hopf algebra H by twisting its product with the help of a cocycle c. The algebra A(H,c) is a flat…

We establish a connection between the theory of cyclotomic ideal class groups and the theory of "geometric" Galois modules and obtain results on the Galois module structure of coherent cohomology groups of Galois covers of varieties over Z.…

We incorporate nonlinear covers of quasisplit reductive groups into the Langlands program, defining an L-group associated to such a cover. This L-group is an extension of the absolute Galois group of a local or global field $F$ by a complex…

In 2018, Legrand and Paran proved a weaker form of the Inverse Galois Problem for all Hilbertian fields and all finite groups: that is, there exist possibly non-Galois extensions over given Hilbertian base field with given finite group as…

We prove a generalization of the fellow traveller property for a certain type of quasi-geodesics and use it to present three equivalent geometric formulations of the bounded reduction property and prove that it is equivalent to preservation…

We wish to attack the problems that H.~Anciaux and K.~Panagiotidou posed in [1], for non-degenerate real hypersurfaces in indefinite complex projective space. We will slightly change these authors' point of view, obtaining cleaner equations…

A group homomorphism $i: H \to G$ is a localization of $H$ if for every homomorphism $\varphi: H\rightarrow G$ there exists a unique endomorphism $\psi: G\rightarrow G$, such that $i \psi=\varphi$ (maps are acting on the right). G\"{o}bel…

We study the cyclic module ${}_SR$ for a ring extension $A \| B$ with centralizer $R$ and bimodule endomorphism ring $S = End {}_BA_B$. We show that if $A \| B$ is an H-separable Hopf subalgebra, then $B$ is a normal Hopf subalgebra of $A$.…

The Hopf-Galois structures admitted by a Galois extension of fields $ L/K $ with Galois group $ G $ correspond bijectively with certain subgroups of $ \mathrm{Perm}(G) $. We use a natural partition of the set of such subgroups to obtain a…

We study the interaction between the group law on an abelian variety and the additive structure induced on its image under a morphism to projective space. Let $A/F$ be a simple abelian variety, $f:A \rightarrow \mathbb{P}^n$ be a morphism…

In this paper we present a reformulation of the Galois correspondence theorem of Hopf Galois theory in terms of groups carrying farther the description of Greither and Pareigis. We prove that the class of Hopf Galois extensions for which…

This paper introduces a systematic approach towards the inverse problem for arboreal Galois representations of finite index attached to quadratic polynomials. Let $F$ be a field of characteristic $\neq 2$, $f\in F[x]$ be monic and quadratic…

The notion of locally quasi-convex abelian group, introduce by Vilenkin, is extended to maximally almost-periodic non-necessarily abelian groups. For that purpose, we look at certain bornologies that can be defined on the set…