Leray's theorem explained

In algebraic topology and algebraic geometry, Leray's theorem (so named after Jean Leray) relates abstract sheaf cohomology with Čech cohomology.

Let

l F be a sheaf on a topological space X and l U an open cover of X. If l F is acyclic on every finite intersection of elements of l U , then \check H ^{q(lU,lF)=} \check H ^{q(X,lF),}

where

\check H ^{q(lU,lF)} is the q -th Čech cohomology group of l F with respect to the open cover l U.

References

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