Leray's theorem

In algebraic topology and algebraic geometry, Leray's theorem (so named after Jean Leray) 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 (meaning that for all and all , then

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

References

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