Geodesic
On the finiteness of Ш for motives associated to modular forms
Documenta mathematica, Tome 2 (1997), pp. 31-46
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Let f be a modular form of even weight on Γ0​(N) with associated motive Mf​. 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 Mf​ is not divisible by p, then the p-part of the Tate-shafarevic group of Mf​ 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.
DOI : 10.4171/dm/22
Classification : 11F66, 11G18, 11R34, 14C15 
@article{10_4171_dm_22,
     author = {Amnon Besser},
     title = {On the finiteness of {{\CYRSH}} for motives associated to modular forms},
     journal = {Documenta mathematica},
     pages = {31--46},
     year = {1997},
     volume = {2},
     doi = {10.4171/dm/22},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/22/}
}
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Amnon Besser. On the finiteness of Ш for motives associated to modular forms. Documenta mathematica, Tome 2 (1997), pp. 31-46. doi: 10.4171/dm/22

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