Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotic behavior of class groups and cyclotomic Iwasawa theory of
  elliptic curves   In this article, we study a relation between certain quotients of ideal class
groups and the cyclotomic Iwasawa module $X_\infty$ of the Pontrjagin dual of
the fine Selmer group of an elliptic curve $E$ defined over $\mathbb{Q}$. We
consider the Galois extension field $K^E_n$ of $\mathbb{Q}$ generated by
coordinates of all $p^n$-torsion points of $E$, and introduce a quotient
$A^E_n$ of the $p$-sylow subgroup of the ideal class group of $K^E_n$ cut out
by the modulo $p^n$ Galois representation $E[p^n]$. We describe the asymptotic
behavior of $A^E_n$ by using the Iwasawa module $X_\infty$. In particular,
under certain conditions, we obtain an asymptotic formula as Iwasawa's class
number formula on the order of $A^E_n$ by using Iwasawa's invariants of
$X_\infty$.

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The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
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The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
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The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
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The categories of this paper are: econ
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The categories of this paper are: math-ph