Related papers: Schopieray's Galois-modular extension conjecture
We show that the Peiffer commutator previously defined by Cigoli, Mantovani and Metere can be used to characterize central extensions of precrossed modules with respect to the subcategory of crossed modules in any semi-abelian category…
In this paper, we classify certain subcategories of modules over a ring R. A wide subcategory of R-modules is an Abelian subcategory of R-Mod that is closed under extensions. We give a complete classification of wide subcategories of…
A central conjecture in inverse Galois theory, proposed by D\`{e}bes and Deschamps, asserts that every finite split embedding problem over an arbitrary field can be regularly solved. We give an unconditional proof of a consequence of this…
This article presents a theory of modules with iterative connection. This theory is a generalisation of the theory of modules with connection in characteristic zero to modules over rings of arbitrary characteristic. We show that these…
We study the noncommutative base change of an entwining structure $(A,C,\psi)$ by a Grothendieck category $\mathfrak S$, using two module like categories. These are the categories of entwined comodule objects and entwined contramodule…
Expanding on the work of Kemp, Ratliff and Shah, for any closure ${\rm cl}$ defined on a class of modules over a Noetherian ring, we develop the theory of ${\rm cl}$-prereductions of submodules. For any interior ${\rm i}$ on a class of…
We introduce Galois Theory for Hopf-Galois Extensions proving existence of a Galois connection between subalgebras of an H-comodule algebra and generalised quotients of the Hopf algebra H. Moreover, we show that these quotients Q which…
Let $A$ be a condensable algebra in a modular tensor category $\mathcal{C}$. We define an action of the fusion category $\mathcal{C}_A$ of $A$-modules in $\mathcal{C}$ on the morphism space $\mbox{Hom}_{\mathcal{C}}(x,A)$ for any $x$ in…
Applying geometric methods of $2$-dimensional cell complex theory, we construct a Galois covering of a bimodule problem satisfying some structure, triangularity and finiteness conditions in order to describe the objects of finite…
Let p be a prime and F(p) the maximal p-extension of a field F containing a primitive p-th root of unity. We give a new characterization of Demuskin groups among Galois groups Gal(F(p)/F) when p=2, and, assuming the Elementary Type…
In this article, we introduce the concepts of graded $s$-prime submodules which is a generalization of graded prime submodules. We study the behavior of this notion with respect to graded homomorphisms, localization of graded modules,…
We investigate modular embeddings for semi-arithmetic Fuchsian groups. First we prove some purely algebro-geometric or even topological criteria for a regular map from a smooth complex curve to a quaternionic Shimura variety to be covered…
We extend the study of the condensed Galois category of a scheme introduced by Barwick, Glasman and Haine in their work on Exodromy. We elaborate its connection to Lurie's work on Ultracategories and provide a description in terms of…
In this paper, we study modular categories whose Galois group actions on their simple objects are transitive. We show that such modular categories admit unique factorization into prime transitive factors. The representations of…
A full subcategory of modules over a commutative ring $R$ is wide if it is abelian and closed under extensions. Hovey \cite{wide} gave a classification of wide subcategories of finitely presented modules over regular coherent rings in terms…
A criterion for M\"uger centralizer of a fusion subcategory of a braided non-degenerate fusion category is given. Along the way we extend some identities on the space of class functions of a fusion category introduced by Shimizu in…
This paper introduces a computational approach to classifying low rank modular categories up to their modular data. The modular data of a modular category is a pair of matrices, $(S,T)$. Virtually all the numerical information of the…
We associate two linear categories with two objects to a module over the subalgebra of coinvariants of a Hopf-Galois extension, and prove that they are isomorphic. The structure Theorem for cleft extensions, and the Militaru \cStefan…
In this paper, we investigate certain submodules in C*-algebras associated to effective \'etale groupoids. First, we show that a submodule generated by normalizers is a closure of the set of compactly supported continuous functions on some…
In previous papers, the Galois module structure of minus class groups was studied for abelian CM extensions. In this paper, we discuss some nonabelian cases, focusing on metacyclic extensions. For a certain class of these, we obtain a…