Related papers: On strong approximation for algebraic groups
The Weak approximation theorem describes the closure of $G(Q)$ inside $G(Q_p)$ as well as inside $G(R)$ for $G$ an algebraic group over $Q$; the closure is always an open normal subgroup with finite abelian quotient, and is well understood…
This is a colloquium style pedagogical introduction to the paradigm of large extra dimensions. To be published in the Proceedings of the Workshop "Crossing the boundaries: Gauge dynamics at strong coupling," (May 14 - 17, 2009,…
This paper gives an explicit argument to show strong boundedness for ${\rm Sp}_{2n}(R)$ for $R$ a ring of S-algebraic integers or a semi-local ring. This gives a quantitative version of a related abstract result in a previous paper of the…
Over the function field of a complex algebraic curve, strong approximation off a non-empty finite set of places holds for the complement of a codimension $2$ closed subset in a homogeneous space under a semisimple algebraic group, and for…
These are my notes for a talk at the The Tate Conjecture workshop at the American Institute of Mathematics in Palo Alto, CA, July 23--July 27, 2007, somewhat revised and expanded. The intent of the talk was to review what is known and to…
In this paper, we study the strong extension groups of Cuntz--Krieger algebras, and present a formula to compute the groups. We also detect the position of the Toeplitz extension of a Cuntz--Krieger algebra in the strong extension group and…
This paper is a follow-up to our joint paper with I. Agol, P. Storm and K. Whyte "Finiteness of arithmetic hyperbolic reflection groups". The main purpose is to investigate the effective side of the method developed there and its possible…
We describe a new approach for classifying conjugacy classes of elementary abelian subgroups in simple algebraic groups over an algebraically closed field, and understanding the normaliser and centraliser structure of these. For toral…
We describe a new type of polycyclic presentations, that we will call refined solvable presentations, for polycyclic groups. These presentations are obtained by refining a series of normal subgroups with abelian sections. These…
We provide a new condition for an absolutely almost simple algebraic group to have good reduction with respect to a discrete valuation of the base field which is formulated in terms of the existence of maximal tori with special properties.…
We construct a finite subgroup of Brauer-Manin obstruction for detecting the existence of integral points on integral models of homogeneous spaces of linear algebraic groups of multiplicative type. As application, the strong approximation…
This is a sequel to arXiv:1308.3604. We study applications to limit multiplicity generalizing the results of arXiv:1208.2257.
This talk presents an overview of the theoretical contributions at the Hard Probes 2013 conference, held in Stellenbosch, South Africa, in November 2013.
The theory of rough sets was firstly introduced by Pawlak (see \cite{p}). Many Mathematician has been studied the relations between rough sets and algebraic systems such as groups, rings and modules. In this paper we will introduce the…
This paper is around the topics I discussed in the lecture I gave at the Isaac Newton Institute in Cambridge, July 2009, in the Introductory Workshop. This paper can be read as a companion to my paper [Sa\"i di], where detailed proofs can…
In May 2015, a conference entitled "Groups, Geometry, and 3-manifolds" was held at the University of California, Berkeley. The organizers asked participants to suggest problems and open questions, related in some way to the subject of the…
We study strong approximation for some algebraic varieties over which are defined using norm forms over the rationals. This allows us to confirm a special case of a conjecture due to Harpaz and Wittenberg.
This is an expanded version of the talk by the author at the conference Polynomial Rings and Affine Algebraic Geometry, February 12--16, 2018, Tokyo Metropolitan University, Tokyo, Japan. Considering a local version of the Zariski…
Generalizing classical extension theory, we solve a Schreier-type extension problem for polygroups by groups. As a consequence, we obtain a method for computing a presentation for a group from its action on a set. The usefulness of this…
This is a survey article on selected topics in approximation theory. The topics either use techniques from the theory of several complex variables or arise in the study of the subject. The survey is aimed at readers having an acquaintance…