Noncommutative Proj and coherent algebras
By Alexander Polishchuk. 2002
61 citations recorded by the source corpus.
We prove that an abelian category equipped with an ample sequence of objects is equivalent to the quotient of the category of coherent modules over the corresponding algebra by the subcategory of finite-dimensional modules. In the Noetherian case a similar result was proved by Artin and Zhang.
Subfields: Algebra and Number Theory, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/019ed0f2510535e07ebd2d17521dd23a7cdc5269
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In Algebra and Number Theory
- Alexander Kuznetsov
- Alexander Polishchuk
- Emanuele Macrì
- P. Stellari
- Yuri Prokhorov
- Constantin Shramov
- Nicolas Addington
- Alexander Perry
In Geometry and Topology
- Alexander Kuznetsov
- Alexander Polishchuk
- Emanuele Macrì
- P. Stellari
- K. Hori
- Arend Bayer
- Alexander Perry
- T. Bridgeland
Citations in the corpus
- Derived categories of quadric fibrations and intersections of quadrics (2005, background): “The first functor is an equivalence by [19], so it remains to consider the second.”
- Classification of holomorphic vector bundles on noncommutative two-tori (2003, background): “Aii = C, Aij = Hom(Ei, Ej) for i 3 ]).”
- Noncommutative two-tori with real multiplication as noncommutative projective varieties (2002, unknown): “A G ] 2 2 D ec”