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Abstract
We study generic objects in triangulated categories and give a characterization of the finite dimensional algebras A such that the derived categories D(Mod A) are generically trivial. This characterization is an analogue of a result of Crawley-Boevey for module categories. As a consequence, we show that D(Mod A) is generically trivial if and only if the category of perfect complexes K b (proj A) is locally finite.
ACKNOWLEDGMENTS
This paper is a part of the author's Ph.D. dissertation, written under the supervision of Professor Henning Krause. The author would like to thank him for suggesting the problem and for many stimulating conversations. The author is also indebted to Claus M. Ringel for many helpful discussions. Finally, the author would like to express his thanks to Xiaowu Chen and Yong Jiang for their comments on previous versions of this paper.
Notes
Communicated by D. Zacharia.