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. 
@article{IM2_2002_66_3_a3,
     author = {S. V. Lapin},
     title = {$(DA)_\infty$-modules over $(DA)_\infty$-algebras and spectral sequences},
     journal = {Izvestiya. Mathematics },
     pages = {543--568},
     publisher = {mathdoc},
     volume = {66},
     number = {3},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2002_66_3_a3/}
}
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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/