Representability of GL_E

2002/04/03 by Nitin Nitsure, Nitsure, Nitin
Mathematics · #14L15 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14L15

paper · pdf · doi:10.48550/arxiv.math/0204047

3 pages, LaTeX

arxiv created 2002/11/27 · arxiv updated 2009/11/30

Abstract

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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