On the (non)vanishing of some "derived" categories of curved dg algebras

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Keller, Bernhard
Lowen, Wendy
Nicolas, Pedro
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Since curved dg algebras, and modules over them, have differentials whose square is not zero, these objects have no cohomology, and there is no classical derived category. For different purposes, different notions of "derived" categories have been introduced in the literature. In this note, we show that for some concrete curved dg algebras, these derived categories vanish. This happens for example for the initial curved dg algebra whose module category is the category of precomplexes, and for certain deformations of dg algebras.
Comment: 18 pages, new title, several local modifications and corrections
Keywords
Mathematics - K-Theory and Homology, Mathematics - Rings and Algebras, 18E30
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