Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Faltings heights of CM cycles and derivatives of L-functions   We study the Faltings height pairing of arithmetic Heegner divisors and CM
cycles on Shimura varieties associated to orthogonal groups. We compute the
Archimedian contribution to the height pairing and derive a conjecture relating
the total pairing to the central derivative of a Rankin L-function. We prove
the conjecture in certain cases where the Shimura variety has dimension 0, 1,
or 2. In particular, we obtain a new proof of the Gross-Zagier formula.

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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: q-alg
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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat
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The categories of this paper are: plasm-ph
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The categories of this paper are: econ
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The categories of this paper are: funct-an
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ex
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The categories of this paper are: eess