Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Uniformity of fibres of period mappings and the $S$-unit equation   In this paper we give a refinement of the method introduced by Lawrence and
Venkatesh and thereby showing that their proof of Mordell's conjecture is
uniform up to a uniform bound on the number of Galois representations attached
to some family of abelian varieties. We are also able to give an unconditional
proof of a uniform boundedness statement on the number of solutions to $S$-unit
equations, which qualitatively is best possible, recovering a result of
Evertse.

24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
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The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
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The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex