Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on the Bilinear Bogolyubov Theorem: Transverse and bilinear sets   A set $P\subset \mathbb{F}_p^n\times\mathbb{F}_p^n$ is called
$\textit{bilinear}$ when it is the zero set of a family of linear and bilinear
forms, and $\textit{transverse}$ when it is stable under vertical and
horizontal sums. A theorem of the first author provides a generalization of
Bogolyubov's theorem to the bilinear setting. Roughly speaking, it implies that
any dense transverse set $P\subset \mathbb{F}_p^n\times\mathbb{F}_p^n$ contains
a large bilinear set. In this paper, we elucidate the extent to which a
transverse set is forced to be (and not only contain) a bilinear set.

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The categories of this paper are: astro-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: econ
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The categories of this paper are: mtrl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: hep-th
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The categories of this paper are: nlin
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The categories of this paper are: eess
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-ex