Geodesic
On the homology of a~tensor product of local rings
Izvestiya. Mathematics , Tome 9 (1975) no. 1, pp. 1-12.

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For quotient rings $A$ and $B$ of a regular ring $R$ the connection between the Hopf algebras $\operatorname{Tor}^A(k,k)$, $\operatorname{Tor}^B(k,k)$ and $\operatorname{Tor}^{A\underset R\otimes R}(k,k)$ is investigated. In general, this connection is expressed by a spectral sequence. Criteria are obtained for $$ \operatorname{Tor}^{A\underset R\otimes R}(k,k)\cong\operatorname{Tor}^A(k,k)\underset{\operatorname{Tor}^R(k,k)}\otimes\operatorname{Tor}^B(k,k). $$ Bibliography: 18 items. 
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L. L. Avramov. On the homology of a~tensor product of local rings. Izvestiya. Mathematics , Tome 9 (1975) no. 1, pp. 1-12. http://geodesic.mathdoc.fr/item/IM2_1975_9_1_a0/

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