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en>Michael Hardy
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en>Mark viking
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Let ''X'' be a scheme (or a stack) with action of a linear algebraic group ''G''. The definition is easy for a locally free sheaf. Let ''F'' be a locally free sheaf on ''X''. Then we can view ''F'' as a vector bundle (with respect to Zariski topology). Then ''F'' is said to equivariant if the action <math>G \times X \to X</math> lifts to that of <math>G \times F \to F</math> so that ''G'' acts on ''F'' and <math>L \to X</math> is equivariant.
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In general, one can define an equivariant sheaf to be an [[equivariant object]] in the category of, say, coherent sheaves.
 
A simple example of an equivariant sheaf is a [[linearlized line bundle]] in [[geometric invariant theory]]. Another example is the sheaf of [[equivariant differential form]]s.
 
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Latest revision as of 01:02, 4 September 2014

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