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Эта публикация цитируется в 342 научных статьях (всего в 342 статьях)
Generators and representability of functors in commutative and noncommutative geometry
A. I. Bondala, M. Van den Berghb a Steklov Mathematical Institute, Russian Academy of Sciences
b Center for Statistics, Hasselt University
Аннотация:
We give a sufficient condition for an Ext-finite triangulated category to be saturated. Saturatedness means that every contravariant cohomological functor of finite type to vector spaces is representable. The condition consists in the existence of a strong generator. We prove that the bounded derived categories of coherent sheaves on smooth proper commutative and noncommutative varieties have strong generators, and are hence saturated. In contrast, the similar category for a smooth compact analytic surface with no curves is not saturated.
Ключевые слова и фразы:
Saturation, generators, representability, triangulated categories.
Статья поступила: 7 марта 2003 г.
Образец цитирования:
A. I. Bondal, M. Van den Bergh, “Generators and representability of functors in commutative and noncommutative geometry”, Mosc. Math. J., 3:1 (2003), 1–36
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/mmj73 https://www.mathnet.ru/rus/mmj/v3/i1/p1
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