Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Arithmetic modularity of special divisors and arithmetic mixed
  Siegel-Weil formula (with an appendix by Yujie Xu)   We refine Kudla's modularity problem for generating series of arithmetic
special divisors on unitary Shimura varieties over CM fields using S. Zhang's
theory of admissible cycles. The admissibility reduces the arithmetic
modularity to an arithmetic mixed Siegel-Weil formula. We prove the arithmetic
modularity when the level at nonsplit place is good and arbitrary at split
places. The innovation in proving the arithmetic mixed Siegel-Weil formula is
to compute arithmetic improper intersections using admissibility and modularity
on the generic fiber.

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The categories of this paper are: supr-con
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The categories of this paper are: nlin
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: alg-geom
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The categories of this paper are: acc-phys
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
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The categories of this paper are: cs
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The categories of this paper are: funct-an
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The categories of this paper are: quant-ph
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The categories of this paper are: q-alg
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The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
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The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga