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
Brandenburg, Martin (2013-10-22). "Rosenberg's Reconstruction Theorem (after Gabber)". arXiv:1310.5978 [math.AG].
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)
Undergraduate Texts in Mathematics
Graduate Studies in Mathematics
Hellenica World - Scientific Library
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