Spin-½: Difference between revisions

Latest revision as of 06:52, 29 December 2014

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-In [[algebraic geometry]], '''Leray's theorem''' relates abstract [[sheaf cohomology]] with [[Čech cohomology]].
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-Let  <math>\mathcal F</math> be a [[sheaf (mathematics)|sheaf]] on a [[topological space]] <math>X</math> and  <math>\mathcal U</math> an [[open cover]] of <math>X.</math> If  <math>\mathcal F</math> is [[acyclic sheaf|acyclic]] on every finite intersection of elements of  <math>\mathcal U</math>, then
-:<math> \check H^q(\mathcal U,\mathcal F)= H^q(X,\mathcal F), </math>
-where  <math>\check H^q(\mathcal U,\mathcal F)</math> is the <math>q</math>-th Čech cohomology group of  <math>\mathcal F</math> with respect to the open cover  <math>\mathcal U.</math>
-== References ==
-* Bonavero, Laurent. ''Cohomology of Line Bundles on Toric Varieties, Vanishing Theorems.'' Lectures 16-17 from "Summer School 2000: Geometry of Toric Varieties."
-{{PlanetMath attribution|id=6328|title=Leray's theorem}}
-[[Category:Sheaf theory]]
-[[Category:Theorems in algebraic geometry]]

Spin-½: Difference between revisions

Latest revision as of 06:52, 29 December 2014

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