Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The local-global principle for divisibility in CM elliptic curves   We consider the local-global principle for divisibility in the Mordell-Weil
group of a CM elliptic curve defined over a number field. For each prime $p$ we
give sharp lower bounds on the degree $d$ of a number field over which there
exists a CM elliptic curve which gives a counterexample to the local-global
principle for divisibility by a power of $p$. As a corollary we deduce that
there are at most finitely many elliptic curves (with or without CM) which are
counterexamples with $p > 2d+1$. We also deduce that the local-global principle
for divisibility by powers of $7$ holds over quadratic fields.

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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
5
The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: cond-mat
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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: hep-ex
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The categories of this paper are: cs
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The categories of this paper are: bayes-an