On the (non)vanishing of some “derived” categories of curved dg algebras |
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Authors: | Bernhard Keller Pedro Nicolás |
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Institution: | a Université Paris Diderot - Paris 7, Institut de Mathématiques de Jussieu, U.M.R. 7586 du CNRS, UFR de Mathématiques, Case 7012, Bâtiment Chevaleret, 75205 Paris Cedex 13, France b Departement Wiskunde-Informatica, Middelheimcampus, Middelheimlaan 1, 2020 Antwerp, Belgium |
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Abstract: | 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 article, 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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Keywords: | 16E40 18D30 |
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