Abstract
For a smashing localisation L of the derived category of a differential graded (dg) algebra A we construct a dg algebra A L and a morphism of dg algebras A→A L that induces the canonical map in cohomology. As a first application we obtain a localisations \(A_{\mathfrak{p}}\) of a dg algebra A with graded commutative homology at a prime ideal \(\mathfrak{p}\) in the homology H * A, namely a morphism \(A\to A_{\mathfrak{p}}\) of dg algebras. As a second application we can use results of Keller to “model” every smashing localisation of compactly generated algebraic triangulated categories by a morphism of dg algebras.
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Brüning, K., Huber, B. Realising Smashing Localisations as Morphisms of DG Algebras. Appl Categor Struct 16, 669–687 (2008). https://doi.org/10.1007/s10485-007-9108-1
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DOI: https://doi.org/10.1007/s10485-007-9108-1