Related papers: Relatively projective profinie groups

We classify all closed 1-connected manifolds $M$ which look like projective planes, i.e. with integral homology $H_*(M)=Z^3$. Furthermore, we give an explicit construction of these manifolds as Thom spaces of open disk bundles.

We construct a projective variety with discrete, non-finitely generated automorphism group. As an application, we show that there exists a complex projective variety with infinitely many non-isomorphic real forms.

In this article we study the homology of nilpotent groups. In particular a certain vanishing result for the homology and cohomology of nilpotent groups is proved.

In this paper we will study the homological properties of various natural modules associated to the Fourier algebra of a locally compact group. In particular, we will focus on the question of identifying when such modules will be projective…

Topological characterization of torus groups is given.

In this paper, we initiate the study of pro-Lie Polish abelian groups from the perspective of homological algebra. We extend to this context the type-decomposition of locally compact Polish abelian groups of Hoffmann and Spitzweck, and…

Let $X$ be surface with isolated singularities in the complex projective space $P^3$ and let denote $Y$ the smooth part of $X$. In this note we discuss some aspects of the topology of such quasi-projective surfaces $Y$: the fundamental…

We give parameterizations of the irreducible representations of finite groups of Lie type in their defining characteristic.

Let $p$ be a prime number, and let $k$ be an algebraically closed field of characteristic $p$. We show that the tame fundamental group of a smooth affine curve over $k$ is a projective profinite group. We prove that the fundamental group of…

We describe free prosoluble subgroups of a free product of profinite groups by strengthening the theorem of Frorian Pop and answering two questions of K. Ersoy and W. Herfort. Relatively projective prosoluble groups are also described.

We study homological approximations of the profinite completion of a limit group (see Thm.~A) and obtain the analogous of Bridson and Howie's Theorem for the profinite completion of a non-abelian limit group (see Thm.~B).

This article uses basic homological methods for evaluating examples of compactly supported cohomology groups of line bundles over projective curve.

We give some background on uniform pro-p groups and the model theory of profinite NIP groups.

We initiate the study of the asymptotic topology of groups that can be realized as fundamental groups of smooth complex projective varieties with holomorphically convex universal covers (these are called here as holomorphically convex…

We say that a group $G$ is of \textit{profinite type} if it can be realized as a Galois group of some field extension. Using Krull's theory, this is equivalent to the ability of $G$ to be equipped with a profinite topology. We also say that…

We completely characterize connected Lie groups all of whose countable subgroups are weakly amenable. We also provide a characterization of connected semisimple Lie groups that are weakly amenable. Finally, we show that a connected Lie…

An isomorphism of symplectically tame smooth pseudocomplex structures on the complex projective plane which is a homeomorphism and differentiable of full rank at two points is smooth.

We show that a profinite group, in which the centralisers of non-trivial elements are metabelian, is either virtually pro-$p$ or virtually soluble of derived length at most 4. We furthermore show that a prosoluble group, in which the…

We characterize the quasiprojective groups that appear as fundamental groups of compact $3$-manifolds (with or without boundary). We also characterize all closed $3$-manifolds that admit good complexifications. These answer questions of…

Our aim is to transfer several foundational results from the modular representation theory of finite groups to the wider context of profinite groups. We are thus interested in profinite modules over the completed group algebra k[[G]] of a…