Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A cohomological classification of vector bundles on smooth affine
  threefolds   We give a cohomological classification of vector bundles of rank $2$ on a
smooth affine threefold over an algebraically closed field having
characteristic unequal to $2$. As a consequence we deduce that cancellation
holds for rank $2$ vector bundles on such varieties. The proofs of these
results involve three main ingredients. First, we give a description of the
first non-stable ${\mathbb A}^1$-homotopy sheaf of the symplectic group.
Second, these computations can be used in concert with F. Morel's ${\mathbb
A}^1$-homotopy classification of vector bundles on smooth affine schemes and
obstruction theoretic techniques (stemming from a version of the Postnikov
tower in ${\mathbb A}^1$-homotopy theory) to reduce the classification results
to cohomology vanishing statements. Third, we prove the required vanishing
statements.

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The categories of this paper are: hep-ph
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The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
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The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph