Points of finite order on an abelian variety

In this paper it is shown that the image of the Galois group under an l-adic representation in the Tate module of an abelian variety has an algebraic Lie algebra which contains the scalar matrices as a subalgebra (Serre’s conjecture). This paper also proves the finiteness of the intersection of a subgroup of an abelian variety all of whose elements have order equal to a power of a fixed number with a wide class of subvarieties. Bibliography: 13 titles.