Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fourier-Jacobi cycles and arithmetic relative trace formula (with an
  appendix by Chao Li and Yihang Zhu)   In this article, we develop an arithmetic analogue of Fourier--Jacobi period
integrals for a pair of unitary groups of equal rank. We construct the
so-called Fourier--Jacobi cycles, which are algebraic cycles on the product of
unitary Shimura varieties and abelian varieties. We propose the arithmetic
Gan--Gross--Prasad conjecture for these cycles, which is related to central
derivatives of certain Rankin--Selberg $L$-functions, and develop a relative
trace formula approach toward this conjecture. As a necessary ingredient, we
propose the conjecture of the corresponding arithmetic fundamental lemma, and
confirm it for unitary groups of rank at most two and for the minuscule case.

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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: dg-ga
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The categories of this paper are: bayes-an
1
The categories of this paper are: cs
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The categories of this paper are: quant-ph
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The categories of this paper are: eess
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The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-th
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The categories of this paper are: econ
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The categories of this paper are: atom-ph