Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Intersection of two quadrics with no common hyperplane in
  $\mathbb{P}^{n}(\mathbb{F}_q)$}}   Let $\mathcal{Q}_1$ and $\mathcal{Q}_2$ be two arbitrary quadrics with no
common hyperplane in ${\mathbb{P}}^n(\mathbb{F}_q)$. We give the best upper
bound for the number of points in the intersection of these two quadrics. Our
result states that $| \mathcal{Q}_1\cap \mathcal{Q}_2|\le 4q^{n-2}+\pi_{n-3}$.
This result inspires us to establish the conjecture on the number of points of
an algebraic set $X\subset {\mathbb{P}}^n(\mathbb{F}_q)$ of dimension $s$ and
degree $d$: $|X(\mathbb{F}_q)|\le dq^s+\pi_{s-1}$.

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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
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The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
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The categories of this paper are: stat
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The categories of this paper are: comp-gas
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The categories of this paper are: astro-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: econ
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The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph
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The categories of this paper are: physics