Realizing modules over the homology of a DGA

• Autores: Gustavo Granja, Sharon Hollander
• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 212, Nº 6, 2008, págs. 1394-1414
• Idioma: inglés
• DOI: 10.1016/j.jpaa.2007.10.007
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• Resumen

  • Let A be a DGA over a field and X a module over H*(A). Fix an A8-structure on H*(A) making it quasi-isomorphic to A. We construct an equivalence of categories between An+1-module structures on X and length n Postnikov systems in the derived category of A-modules based on the bar resolution of X. This implies that quasi-isomorphism classes of An-structures on X are in bijective correspondence with weak equivalence classes of rigidifications of the first n terms of the bar resolution of X to a complex of A-modules. The above equivalences of categories are compatible for different values of n. This implies that two obstruction theories for realizing X as the homology of an A-module coincide.