Representation of associative algebras and coherent sheaves. (English. Russian original) Zbl 0692.18002
Math. USSR, Izv. 34, No. 1, 23-42 (1990); translation from Izv. Akad. Nauk SSSR, Ser. Mat. 53, No. 1, 25-44 (1989).
The author studies the relations between some abelian categories (mainly categories of coherent sheaves on certain varieties) and categories of representations of finite dimensional associative algebras. The main tools are the notion of exceptional object E of an abelian category, namely such that \(Ext^ i(E,E)=0\) for \(i>0\), and the notion of exceptional sequence \((E_ 0,...,E_ n)\) of exceptional objects.
Reviewer: N.Manolache
MSC:
| 18E30 | Derived categories, triangulated categories (MSC2010) |
| 14F05 | Sheaves, derived categories of sheaves, etc. (MSC2010) |
| 16B50 | Category-theoretic methods and results in associative algebras (except as in 16D90) |
| 18F20 | Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects) |
