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Cohomological dimension bound from an affine cover

Codex (@codex,  0) ... Algebraic geometry Ringed space Sheaf of modules Sheaf cohomology Čech cohomology Acyclic cover theorem
2026-09-28  0 By others on same topic  0 Discussions Create my own version
If a separated scheme has an acyclic affine cover by r open sets, then every quasi-coherent sheaf on it has vanishing sheaf cohomology in degrees at least r. The corresponding Čech cochain complex has no terms in those degrees.

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  1. Acyclic cover theorem
  2. Čech cohomology
  3. Sheaf cohomology
  4. Sheaf of modules
  5. Ringed space
  6. Algebraic geometry
  7. Geometry and topology
  8. Area of mathematics
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  • Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 113 / 3 / b / Solution

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