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Perfect Derived Categories of Positively Graded DG Algebras

Abstract

We investigate the perfect derived category \({{\rm dgPer}}(\mathcal{A})\) of a positively graded differential graded (dg) algebra \(\mathcal{A}\) whose degree zero part is a dg subalgebra and semisimple as a ring. We introduce an equivalent subcategory of \({{{\rm dgPer}}}(\mathcal{A})\) whose objects are easy to describe, define a t-structure on \({{{\rm dgPer}}}(\mathcal{A})\) and study its heart. We show that \({{{\rm dgPer}}}(\mathcal{A})\) is a Krull–Remak–Schmidt category. Then we consider the heart in the case that \(\mathcal{A}\) is a Koszul ring with differential zero satisfying some finiteness conditions.

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Correspondence to Olaf M. Schnürer.

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Supported by a grant of the state of Baden-Württemberg.

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Schnürer, O.M. Perfect Derived Categories of Positively Graded DG Algebras. Appl Categor Struct 19, 757–782 (2011). https://doi.org/10.1007/s10485-010-9221-4

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Keywords

  • Differential graded module
  • DG module
  • t-structure
  • Heart
  • Koszul duality

Mathematics Subject Classifications (2000)

  • 18E30
  • 16D90