Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the structure of Selmer and Shafarevich-Tate groups of higher weight
  modular forms   Under a non-torsion assumption on Heegner points, results of Kolyvagin
describe the structure of Shafarevich-Tate groups of elliptic curves. In this
paper we prove analogous results for ($p$-primary) Shafarevich-Tate groups
associated with higher weight modular forms over imaginary quadratic fields
satisfying a "Heegner hypothesis". More precisely, we show that the structure
of Shafarevich-Tate groups is controlled by cohomology classes built out of
Nekov\'a\v{r}'s Heegner cycles on Kuga-Sato varieties. As an application of our
main theorem, we improve on a result of Besser giving a bound on the order of
these groups. As a second contribution, we prove a result on the structure of
($p$-primary) Selmer groups of modular forms in the sense of Bloch--Kato.

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The categories of this paper are: math-ph
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The categories of this paper are: q-alg
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The categories of this paper are: funct-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: nlin
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph
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The categories of this paper are: econ
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
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The categories of this paper are: astro-ph
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The categories of this paper are: physics
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The categories of this paper are: hep-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci