Relative fundamental groups and rational points

Fundamental Functor Based on Hypergroups and Groups

The purpose of this paper is to compute of fundamental relations of hypergroups. In this regards first we study some basic properties of fundamental relation of hypergroups, then we show that any given group is isomorphic to the fundamental group of a nontrivial hypergroup. Finally we study the connections between categories of hypergroups and groups via the fundam...

Nearly Rational Frobenius Groups

In this paper, we study the structure of nite Frobenius groups whose non-rational or non-real irreducible characters are linear.

Multiple Mixing for Adele Groups and Rational Points

We prove an asymptotic formula for the number of rational points of bounded height on projective equivariant compactifications of H\G, where H is a connected simple algebraic group embedded diagonally into G := H. Introduction Let X ⊂ P be a smooth projective variety over a number field F . Fix a height function (1) H : P(F )→R>0 and consider the counting function N(X,T ) := {x ∈ X(F ) |H(x) ≤ ...

Symmetric Squares of Elliptic Curves: Rational Points and Selmer Groups

Groups of Rational Points on Abelian Varieties over Finite Fields

Fix an isogeny class of abelian varieties with commutative endomorphism algebra over a finite field. This isogeny class is determined by a Weil polynomial fA without multiple roots. We give a classification of groups of rational points on varieties from this class in terms of Newton polygons of fA(1− t).