Homology, Homotopy and Applications

Volume 9 (2007)

Number 2

Thick subcategories of the derived category of a hereditary algebra

Pages: 165 – 176

DOI: http://dx.doi.org/10.4310/HHA.2007.v9.n2.a7

Author

Kristian Brüning (Universität Paderborn, Germany)

Abstract

We classify thick subcategories of the bounded derived category of a hereditary abelian category $A$ in terms of subcategories of $A$. The proof can be applied to characterize the localizing subcategories of the full derived category of $A$. As an application we prove an algebraic analog of the telescope conjecture for the derived category of a representation finite hereditary artin algebra.

Keywords

thick subcategory; hereditary; smashing conjecture; localizing subcategory; derived category

2010 Mathematics Subject Classification

16G20, 18E30

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