Alexandru Buium (New Mexico) <BR> <BR>


<B>Abstract</b>: <BR>
Given a  correspondence between a modular curve and an
elliptic curve A we show that there are not too many 
relations among the CM-points of A.
In particular we show that the intersection of any finite rank
subgroup of A with the set
of CM-points of A is finite. We will also present  a local version of this global
result with
an effective bound
valid also for certain infinite rank subgroups. 
 Furthermore we
will give similar global and local results
for intersections between subgroups of A and
isogeny classes in A.
The local results are proved using a technique based on
"ordinary arithmetic differential equations".
All of this is joint work with B.
Poonen. <BR>