FORMAL DRINFELD MODULES AND ALGEBRAICITY

Let P(t) is an element of F-q[t] be a monic prime polynomial of degree n and let F-q[t](P) be the completion of F-q[t] for the P(t)-adic val uation. For each formal Drinfeld module Phi : F-q[t](P) --> F-q[t](P){ {sigma}} of rank 1, we can define the reduced module (when the reducti on is not trivial) <(Phi)over bar> : F-q[t](P) -- > F(q)n{{sigma}}, wh ere F(q)n = F-q[t](P)/(P). Let R(t) is an element of F-q[t](P). If <(P hi)over bar>(R)(T) is the power series which represents the action of <(Phi)over bar> : EndF(q)n (<(Phi)over bar>) on a transcendantal eleme nt T, we establish the following result: <(Phi)over bar>T-R is algebra ic over F(q)n(T) if and only if R(t) is an element of F-q(t). (C) Acad emie des Sciences/Elsevier, Paris