Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A lower bound for the canonical height on elliptic curves over abelian
  extensions   Let E/K be an ellptic curve defined over a number field, let h be the
canonical height on E, and let K^ab be the maximal abelian extension of K.
Extending work of M. Baker, we prove that there is a positive constant C(E/K)
so that every nontorsion point P in E(K^ab) satisfies h(P) > C(E/K).

20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
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The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
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The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
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The categories of this paper are: q-alg