15 citations · 33 across the 21 of their papers we have counts for
12 papers · 1 filter
Arithmetic Teichmuller Theory
Arash Rastegar
By Grothendieck's anabelian conjectures, Galois representations landing in outer automorphism group of the algebraic fundamental group which are associated to hyperbolic smooth cur…
Approximation on abelian varieties by its subgroups
Arash Rastegar
In this paper, we introduce an algebro-geometric formulation for Faltings' theorem on diophantine approximation on abelian varieties using an improvement of Faltings-Wustholz obser…
A geometric formulation of Siegel's diophantine theorem
Arash Rastegar
In this paper, we introduce an algebro-geometric formulation for Siegel's theorem using an improvement of Lang's version of Roth's theorem over finitely generated fields of charact…
Arithmetic Deformation Theory of Lie Algebras
Arash Rastegar
This paper is devoted to deformation theory of graded Lie algebras over or with finite dimensional graded pieces. Such deformation problems naturally appear in number t…
Self-Similarity in Geometry, Algebra and Arithmetic
Arash Rastegar
We define the concept of self-similarity of an object by considering endomorphisms of the object as `similarity' maps. A variety of interesting examples of self-similar objects in…
On Profinite Hyperbolicity and Diophantine Geometry
Arash Rastegar
In this note, we explore the notion of hyperbolicity of topologically finitely generated profinite groups. Some applications to diophantine geometry are suggested and we try to ref…
Deformation of Outer Representations of Galois Group II
Arash Rastegar
This paper is devoted to deformation theory of "anabelian" representations of the absolute Galois group landing in outer automorphism group of the algebraic fundamental group of a…
On a Theorem of Ihara
Arash Rastegar
Let be a prime number and let be a positive integer prime to . By an Ihara result we mean existence of an injection with torsion-free cokernel from a full lattice in the…
On Atkin-Lehner correspondences on Siegel spaces
Arash Rastegar
We introduce a higher dimensional Atkin-Lehner theory for Siegel-Parahoric congruence subgroups of . Old Siegel forms are induced by geometric correspondences on Siegel mo…
On Congruences Between Drinfeld Modular Forms
Arash Rastegar
Let denote a finite field of characteristic and let be an effective divisor on the affine line over and let be a point on the affine lin…
Deformation of Outer Representations of Galois Group
Arash Rastegar
To a hyperbolic smooth curve defined over a number-field one naturally associates an "anabelian" representation of the absolute Galois group of the base field landing in outer auto…
Self-Similar Fractals and Arithmetic Dynamics
Arash Rastegar
The concept of self-similarity on subsets of algebraic varieties is defined by considering algebraic endomorphisms of the variety as `similarity' maps. Self-similar fractals are su…