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. 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
References
- Brandenburg, Martin (2013-10-22). "Rosenberg's Reconstruction Theorem (after Gabber)". arXiv:1310.5978 .
- Gabriel, Pierre (1962). "Des catégories abéliennes". Bulletin de la Société Mathématique de France. 90: 323–448. doi:10.24033/bsmf.1583.
External links
- https://ncatlab.org/nlab/show/Gabriel-Rosenberg+theorem
- How to unify various reconstruction theorems (Gabriel-Rosenberg, Tannaka, Balmers)
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