Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $\mathbb{A}^1$-connected components of blow-up of threefolds fibered
  over a surface   Over a perfect field, we determine the sheaf of $\mathbb{A}^1$-connected
components of a class of threefolds given by the Blow-up of a variety admitting
a $\mathbb{P}^1$-fibration over either an $\mathbb{A}^1$-rigid or a
non-uniruled surface, along a smooth curve. As a consequence, we verify that
the sheaf of $\mathbb{A}^1$-connected components for such varieties is
$\mathbb{A}^1$-invariant.

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The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: plasm-ph
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The categories of this paper are: stat
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The categories of this paper are: astro-ph
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The categories of this paper are: q-bio
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The categories of this paper are: nlin
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The categories of this paper are: econ
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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
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The categories of this paper are: q-alg