for motives associated to modular forms
for motives associated to modular forms
Let f be a modular form of even weight on 
with
associated motive 
. Let K be a
quadratic imaginary field satisfying certain standard conditions. We
improve a result of Nekovár and prove that
if a rational prime p is outside a finite set of primes depending
only on the form
f, and if the image of the Heegner
cycle associated with K in the p-adic intermediate jacobian of
is not divisible by p, then the p-part of the
Tate-Shafarevic group of over K
is trivial.
An important ingredient of this work is an analysis of the behavior of
``Kolyvagin test classes'' at primes dividing the level N.
In addition, certain complications, due to the possibility of f having a
Galois conjugate self-twist, have to be dealt with.
1991 Mathematics Subject Classification: 11G18, 11F66, 11R34, 14C15.