Alexandru Buium (New Mexico)
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
an effective bound
valid also for certain infinite rank subgroups.
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.