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 , 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."
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Categories:
- Sheaf theory
- Theorems in algebraic geometry
- Theorems in algebraic topology
- Abstract algebra stubs