Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on the Mordell-Weil rank modulo n   Conjecturally, the parity of the Mordell-Weil rank of an elliptic curve over
a number field K is determined by its root number. The root number is a product
of local root numbers, so the rank modulo 2 is conjecturally the sum over all
places of K of a function of elliptic curves over local fields. This note shows
that there can be no analogue for the rank modulo 3, 4 or 5, or for the rank
itself. In fact, standard conjectures for elliptic curves imply that there is
no analogue modulo n for any n>2, so this is purely a parity phenomenon.

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The categories of this paper are: hep-lat
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The categories of this paper are: supr-con
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The categories of this paper are: gr-qc
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The categories of this paper are: mtrl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: econ
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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga