Jump to content

Leray's theorem

From Wikipedia, the free encyclopedia
(Redirected from Leray 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 , then

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

References

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

This article incorporates material from Leray's theorem on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.