Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sato-Tate groups of genus 2 curves   We describe the analogue of the Sato-Tate conjecture for an abelian variety
over a number field; this predicts that the zeta functions of the reductions
over various finite fields, when properly normalized, have a limiting
distribution predicted by a certain group-theoretic construction related to
Hodge theory, Galois images, and endomorphisms. After making precise the
definition of the "Sato-Tate group" appearing in this conjecture, we describe
the classification of Sato-Tate groups of abelian surfaces due to
Fite-Kedlaya-Rotger-Sutherland. (These are notes from a three-lecture series
presented at the NATO Advanced Study Institute "Arithmetic of Hyperelliptic
Curves" held in Ohrid (Macedonia) August 25-September 5, 2014, and are expected
to appear in a proceedings volume.)

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The categories of this paper are: chem-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
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The categories of this paper are: stat
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-th