Geodesic
Homological determinacy of $p$-adic representations of rings with
Izvestiya. Mathematics , Tome 4 (1970) no. 5, pp. 1001-1016.

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For rings with power basis it is proved that if two modules which are free and finitely generated over the ring of $p$-adic integers have cohomology of identical behavior, then they are “almost isomorphic”. 
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A. V. Yakovlev. Homological determinacy of $p$-adic representations of rings with. Izvestiya. Mathematics , Tome 4 (1970) no. 5, pp. 1001-1016. http://geodesic.mathdoc.fr/item/IM2_1970_4_5_a2/

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