Proof of Manin’s theorem by reduction to positive characteristic

Abstract

We explain in this note how to deduce a characteristic 0 Mordell-Lang statement for function fields from the positive characteristic version. See the contributions of Bouscaren and Hindry to this volume for the general statement of Mordell-Lang. (See also [Lan 91] for the history and further references.) While we see no obstacle to proving the general statement by the same method, we will restrict the statement to abelian varieties and rational points.