Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Iwasawa-Greenberg main conjecture for non-ordinary modular forms and
  Eisenstein congruences on $\mathrm{GU}(3,1)$   In this paper we prove one side divisibility of the Iwasawa-Greenberg main
conjecture for Rankin-Selberg product of a weight two cusp form and an ordinary
CM form of higher weight, using congruences between Klingen Eisenstein series
and cusp forms on $\mathrm{GU}(3,1)$, generalizing earlier result of the
third-named author to allow non-ordinary cusp forms. The main result is a key
input in the third author's proof for Kobayashi's $\pm$-main conjecture for
supersingular elliptic curves. The new ingredient here is developing a
semi-ordinary Hida theory along an appropriate smaller weight space, and a
study of the semi-ordinary Eisenstein family.

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The categories of this paper are: eess
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The categories of this paper are: chem-ph
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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: adap-org
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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: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: astro-ph
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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: comp-gas
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The categories of this paper are: math-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th