Sheaf
Summary
A sheaf on a topological space assigns to each open set a set of data, such as functions, with restriction maps to smaller open sets. The data must be determined by their local pieces, and compatible local pieces must glue together. Sheaves organise local information on a space and measure how it fails to be global. They are the language of modern algebraic geometry, where a scheme is a space with a sheaf of rings. They are also the coefficients of sheaf cohomology in topology and complex analysis.
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About this page
| Tag | TB6TM6R4MD |
|---|---|
| URI | m2://TB6TM6R4MD |
| Kind | concept |
| Writing | W0 stub |
| MSC | 54B40, 18F20, 14F06 |
| Same as |
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Used by
- Ringed space
- Adic space
- Sheaf of modules
- Locally ringed space
- Brelot space
- Graded manifold
- Sheaf cohomology
- Rigid analytic space
- Closed immersion
- Affine scheme
- Stalk
- Algebraic space
- Cartier divisor
- Perverse sheaf
- Banach analytic space
- Complex analytic space
- Supermanifold
- Čech cohomology
- Harmonic space