Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Canonical Kahler metrics and Arithmetics -- Generalising Faltings
  heights   We extend the Faltings modular heights of abelian varieties to general
arithmetic varieties and show direct relations with the Kahler-Einstein
geometry, the Minimal Model Program, heights of Bost and Zhang, and give some
applications. Along the way, we propose arithmetic Yau-Tian-Donaldson
conjecture, an equivalence of a purely arithmetic property of variety and its
metrical property, and partially confirm it.

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The categories of this paper are: funct-an
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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: adap-org
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The categories of this paper are: plasm-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: cs
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The categories of this paper are: patt-sol
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn