Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Heights, ranks and regulators of abelian varieties   We lower bound the Faltings height of an abelian variety over a number field
by the sum of its injectivity diameter and the norm of its bad reduction
primes. It leads to an unconditional bound on the rank of Mordell-Weil groups.
Assuming the height conjecture of Lang and Silverman, we then obtain a
Northcott property for the regulator on the set of simple abelian varieties
defined over a fixed number field, of fixed dimension $g$, bounded rank and
with dense rational points over a number field. We remove the simplicity
assumption in the principally polarized case by giving a refined version of the
Lang-Silverman conjecture.

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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: q-bio
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The categories of this paper are: hep-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
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The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex