Representability of $GL_E$

Details Representability of $GL_E$ Representability of $GL_E$

2002-04-03

arxiv.org/abs/math/0204047v2

Mathematics

Algebraic Geometry

3 pages, LaTeX

Scientific paper

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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