Geodesic
Homological determination of $\Gamma$-modules
Zapiski Nauchnykh Seminarov POMI, Rings and modules, Tome 64 (1976), pp. 104-126

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It is proved that if $M$ is a profinitely generated $\Gamma$-module which is free as a module over the ring of $p$-adic integers, then $M$ is determined up to free direct factors by its homology. This result generalizes the theorem on homological determinacy of $p$-adic representations of a cyclic group [Ref. Zh. Mat., 3A, 318 (1971)]. 
@article{ZNSL_1976_64_a10,
     author = {Yu. S. Sarkisyan and A. V. Yakovlev},
     title = {Homological determination of $\Gamma$-modules},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {104--126},
     publisher = {mathdoc},
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     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1976_64_a10/}
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Yu. S. Sarkisyan; A. V. Yakovlev. Homological determination of $\Gamma$-modules. Zapiski Nauchnykh Seminarov POMI, Rings and modules, Tome 64 (1976), pp. 104-126. http://geodesic.mathdoc.fr/item/ZNSL_1976_64_a10/