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

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

2009-05-23

arxiv.org/abs/0905.3845v2

Mathematics

K-Theory and Homology

18 pages, new title, several local modifications and corrections

Scientific paper

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.

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