导出范畴的生成元和维数
Generators and dimensions of derived categories
摘要：
几年前，Bondal，Rouquier和Van den Bergh引入了三角范畴维数的概念，Rouquier证明了完满域上有限型分离有限型概形上凝聚层的有界导出范畴具有有限维数.本文研究交换诺特环上有限生成模的有界导出范畴的维数。本文的主要结果是：它在包含具有完全剩余域的域的完全局部环上是有限的。我们的方法也给出了一个环理论证明的仿射的情况下，Rouquier定理。
英文摘要：
Several years ago, Bondal, Rouquier and Van den Bergh introduced the notion of the dimension of a triangulated category, and Rouquier proved that the bounded derived category of coherent sheaves on a separated scheme of finite type over a perfect field has finite dimension. In this paper, we study the dimension of the bounded derived category of finitely generated modules over a commutative Noetherian ring. The main result of this paper asserts that it is finite over a complete local ring containing a field with perfect residue field. Our methods also give a ring-theoretic proof of the affine case of Rouquier's theorem.
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