Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Representability of $GL_E$   Let $S$ be a noetherian scheme, and let $E$ be a coherent sheaf on it. We
define a group-valued contravariant functor $GL_E$ on $S$-schemes by
associating to any $S$-scheme $T$ the group $GL_E(T)$ of all linear
automorphisms of the pullback of $E$ to $T$. This functor is clearly a sheaf in
the fpqc topology. We prove that $GL_E$ is representable by a group-scheme over
$S$ if and only if the sheaf $E$ is locally free.

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The categories of this paper are: nucl-th
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: eess
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The categories of this paper are: nlin
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The categories of this paper are: hep-th
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The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: q-fin