Gabriel–Rosenberg reconstruction theorem
In algebraic geometry, the Gabriel–Rosenberg reconstruction theorem, introduced in (Gabriel 1962), states that a quasi-separated scheme can be recovered from the category of quasi-coherent sheaves on it.[1] The theorem is taken as a starting point for noncommutative algebraic geometry as the theorem says (in a sense) working with stuff on a space is equivalent to working with the space itself. It is named after Pierre Gabriel and Alexander L. Rosenberg.
See also[]
- Tannakian duality
References[]
- Pierre Gabriel, Des catégories abéliennes, Bulletin de la Société Mathématique de France, 90 (1962), pp. 323–448.
External links[]
- https://ncatlab.org/nlab/show/Gabriel-Rosenberg+theorem
- How to unify various reconstruction theorems (Gabriel-Rosenberg, Tannaka,Balmers)
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- Theorems in algebraic geometry
- Scheme theory
- Sheaf theory