Generically trivial derived categories

TL;DR

This paper characterizes when derived categories of modules over finite dimensional algebras are generically trivial, linking this property to local finiteness of perfect complexes, thus extending Crawley-Boevey's results.

Contribution

It provides a new characterization of generically trivial derived categories for finite dimensional algebras, connecting it to the local finiteness of perfect complexes.

Findings

Derived categories are generically trivial iff perfect complexes form a locally finite category.

Extends Crawley-Boevey's results from module categories to derived categories.

Provides criteria for triviality of derived categories in algebra representation theory.

Abstract

We study generic objects in triangulated categories and characterize the finite dimensional algebras $A$ such that the derived categories $D(\Mod A)$ are generically trivial. This 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.