Geodesic
$(DA)_\infty$-modules over $(DA)_\infty$-algebras and spectral sequences
Izvestiya. Mathematics , Tome 66 (2002) no. 3, pp. 543-568.

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We introduce the construction of a $(DA)_\infty$-(co)module over a $(DA)_\infty$-(co) algebra and study its main homotopy properties. We establish a connection between $(DA)_\infty$-(co)modules over $(DA)_\infty$-(co)algebras and spectral sequences, and thus obtain the structure of an $A_\infty$-comodule over the Milnor $A_\infty$-coalgebra on the homology of any spectrum directly from the differentials of the Adams spectral sequence of this spectrum. 
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     title = {$(DA)_\infty$-modules over $(DA)_\infty$-algebras and spectral sequences},
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S. V. Lapin. $(DA)_\infty$-modules over $(DA)_\infty$-algebras and spectral sequences. Izvestiya. Mathematics , Tome 66 (2002) no. 3, pp. 543-568. http://geodesic.mathdoc.fr/item/IM2_2002_66_3_a3/

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