Amnon Besser

摘要

Let $f$ be a modular form of even weight on $Gamma_0(N)$ withassociated motive $mathcal{M}_f$. Let $K$ be aquadratic imaginary field satisfying certain standard conditions. We improve a result of Nekovar{} and prove thatif a rational prime $p$ is outside a finite set of primes depending only on the form$f$, and if the image of the Heegnercycle associated with $K$ in the $p$-adic intermediate Jacobian of$mathcal{M}_f$ is not divisible by $p$, then the $p$-part of theTate-shafarevic{} group of $mathcal{M}_f$ 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 aGalois conjugate self-twist, have to be dealt with.