Geodesic
On the finiteness of ${\cyr Sh}$ for motives associated to modular forms
Documenta mathematica, Tome 2 (1997), pp. 31-46.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Let $f$ be a modular form of even weight on $\Gamma_0(N)$ with associated motive $\mathcal{M}_f$. Let $K$ be a quadratic imaginary field satisfying certain standard conditions. We improve a result of Nekovar 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 $\mathcal{M}_f$ is not divisible by $p$, then the $p$-part of the Tate-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 a Galois conjugate self-twist, have to be dealt with.
Classification : 11G18, 11F66, 11R34, 14C15 
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     author = {Besser, Amnon},
     title = {On the finiteness of ${\cyr Sh}$ for motives associated to modular forms},
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     volume = {2},
     year = {1997},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_1997__2__a13/}
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Besser, Amnon. On the finiteness of ${\cyr Sh}$ for motives associated to modular forms. Documenta mathematica, Tome 2 (1997), pp. 31-46. http://geodesic.mathdoc.fr/item/DOCMA_1997__2__a13/