The telescope conjecture for derived categories arising in representation theory

对于表征理论中出现的范畴，我们将研究三角化范畴的望远镜猜想。我们遵循尼曼的原始方法，并在适当的微分梯度代数上建立派生范畴的分层。另一个有希望的方法是Krause和Stovicek对遗传环的派生范畴的方法。积极的结果将特别应用于有限维代数的表示，例如在上同调支持变体或分类厚和局部化子类别的背景下。

The telescope conjecture for triangulated categories will be studied for categories arising in representation theory. We follow the original approach of Neeman and establish a stratification of derived categories over appropriate differential graded algebras. Another promising approach is that of Krause and Stovicek for derived categories of hereditary rings. Positive results will be applied in particular to representations of finite dimensional algebras, for instance in the context of cohomological support varieties or for classifying thick and localizing subcategories.