Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Modularity and Heights of CM cycles on Kuga-Sato varieties   We prove a higher weight general Gross-Zagier formula for CM cycles on
Kuga-Sato varieties over the modular curve X(N). To formulate and prove this
result, we prove the modularity of CM cycles, in the sense that the Hecke
modules they generate are semisimple whose irreducible components are
associated to higher weight holomorphic cuspidal automorphic representations of
GL2,Q. The higher weight general Gross-Zagier formula is proved using
arithmetic relative trace formulas. The proof of the modularity of CM cycles is
inspired by arithmetic theta lifting.

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The categories of this paper are: physics
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The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci
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The categories of this paper are: math-ph
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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: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: quant-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: gr-qc