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arXiv · 1607.02609

Dualizable and semi-flat objects in abstract module categories

Rune Harder Bak
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Abstract

In this paper, we define what it means for an object in an abstract module category to be dualizable and we give a homological description of the direct limit closure of the dualizable objects. Our description recovers existing results of Govorov and Lazard, Oberst and R{\"o}hrl, and Christensen and Holm. When applied to differential graded modules over a differential graded algebra, our description yields that a DG-module is semi-flat if and only if it can be obtained as a direct limit of finitely generated semi-free DG-modules. We obtain similar results for graded modules over graded rings and for quasi-coherent sheaves over nice schemes.

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Rune Harder Bak. 2016-07-09. Dualizable and semi-flat objects in abstract module categories. https://arxiv.org/abs/1607.02609

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