  The classic Schneider-Lang theorem in transcendence theory asserts that there
are only finitely many points at which algebraically independent complex
meromorphic functions of finite order of growth can simultaneously take values
in a number field, when satisfying a polynomial differential equation with
coefficients in this given number field. In this article, we are interested in
generalizing this theorem in two directions. First, instead of considering
meromorphic functions on C we consider holomorphic maps on an affine curve over
the field C or C_p. This extends a statement of D. Bertrand, which applies to
meromorphic functions on P^1(C) or P^1(C_p) minus a finite subset of points.
Secondly, we deal with algebraic values taken by the functions, instead of
rational values as in the classic setting, inspired by a work of D. Bertrand.
We prove a geometric statement extending those two results, using the slopes
method, written in the language of Arakelov geometry. In the complex case, we
recover a special case of a result by C. Gasbarri.
