Leray's theorem

Leray's theorem

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

Let mathcal F be a sheaf on a topological space X and mathcal U={U_i} a countable cover of X. If mathcal F is acyclic on every finite intersection of elements of mathcal U, then

: check H^q(mathcal U,mathcal F)=check H^q(X,mathcal F),

where check H^q(mathcal U,mathcal F) is the q-th Cech cohomology group of mathcal F with respect to the open cover mathcal U.

References

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

ee also

* sheaf (mathematics)
* sheaf cohomology

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