Leray's theorem

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In algebraic geometry, Leray's theorem relates abstract sheaf cohomology with Čech cohomology.

Let be a sheaf on a topological space and an open cover of If is acyclic on every finite intersection of elements of , then

where is the -th Čech cohomology group of with respect to the open cover


  • Bonavero, Laurent. Cohomology of Line Bundles on Toric Varieties, Vanishing Theorems. Lectures 16-17 from "Summer School 2000: Geometry of Toric Varieties."

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