À propos de G. A. G. R.
Let be a prime number, the field of -adic numbers and the completion of the algebraic closure of . In this paper we obtain a representation theorem for rigid analytic functions on which are equivariant with respect to the Galois group , where is a lipschitzian element of and denotes the -neighborhood of the -orbit of .
The aim of this paper is to extend our previous results about Galois action on the torsion points of abelian varieties to the case of (finitely generated) fields of characteristic 2.
We estimate the fraction of isogeny classes of abelian varieties over a finite field which have a given characteristic polynomial modulo . As an application we find the proportion of isogeny classes of abelian varieties with a rational point of order .