en>Mark viking: /* top */ Added wl, moved one wl to first occurence

2014-09-03T23:02:55Z

top: Added wl, moved one wl to first occurence

← Older revision		Revision as of 01:02, 4 September 2014
Line 1:		Line 1:
	~~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~~.		Mine Deputy Sampley from Stanstead, has hobbies and interests such as fencing, property developers in singapore and train collecting. In recent time took some time to journey to and its Po Delta.<br><br>Also visit my web blog apartment for sale ([http://www.pagefitness.com/?option=com_k2&view=itemlist&task=user&id=87559 mouse click the up coming website page])

	~~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.~~

	~~{{geometry-stub}}~~

en>Michael Hardy at 00:13, 15 December 2013

2013-12-15T00:13:18Z

New page

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.

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.

{{geometry-stub}}

Combinant - Revision history

en>Mark viking: /* top */ Added wl, moved one wl to first occurence

en>Michael Hardy at 00:13, 15 December 2013