Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The inverse deformation problem   We show the inverse deformation problem has an affirmative answer: given a
complete local noetherian ring $A$ with finite residue field $\pmb{k}$, we show
that there is a topologically finitely generated profinite group $\Gamma$ and
an absolutely irreducible continuous representation $\bar\rho:\Gamma\to
GL_n(\pmb{k})$ such that $A$ is the universal deformation ring for
$\Gamma,\bar\rho$.

4
The categories of this paper are: cond-mat
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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
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The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-bio
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol