# anonymous

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 Jan12 awarded Popular Question Jan7 awarded Yearling Jan5 awarded Popular Question Aug8 awarded Nice Question Jun19 accepted Reference request: Tensor product of DG-modules Jun19 comment Reference request: Tensor product of DG-modules Thanks, rational homotopy theory has the construction I was looking for Jun19 comment Reference request: Tensor product of DG-modules Just to be sure, Osborne's book discusses tensor products over a DG-algebra? Jun19 asked Reference request: Tensor product of DG-modules May24 revised Finite projective dimension and vanishing of ext on f.g modules added 197 characters in body May22 comment Finite projective dimension and vanishing of ext on f.g modules I see. Thanks. Do you have an answer to the originial question? May22 asked Finite projective dimension and vanishing of ext on f.g modules May16 comment $H_{I}^{n}(M)\cong H_{I}^{n}(R)\otimes_R M.$ Note that $C(a,R)$ is a complex of flat modules. May15 comment $H_{I}^{n}(M)\cong H_{I}^{n}(R)\otimes_R M.$ In general you can read for example in Weibel's homological algebra. But for now - by total derived functor I just mean that you skip the last step in constructing derived functors, that is - don't take cohomology May15 comment $H_{I}^{n}(M)\cong H_{I}^{n}(R)\otimes_R M.$ If $R$ is noetherian, $a_1,\dots,a_n$ is a sequence that generates $I$, and $C(a_1,\dots,a_n)$ is the Cech complex associated to this sequence, then there is a functorial isomorphism in the derived category $R\Gamma_I(M) \cong M\otimes C(a_1,\dots,a_n)$. Thus what you asked in the comment follows from associtiviaty of the tensor product. May15 comment What is the derivative of $\ln(4^x)$? as you said, $ln(4^x)$ = $xln4$, so its derivative is simply $ln4$. May15 revised $H_{I}^{n}(M)\cong H_{I}^{n}(R)\otimes_R M.$ edited tags May15 answered $H_{I}^{n}(M)\cong H_{I}^{n}(R)\otimes_R M.$ May7 awarded Caucus Apr19 awarded Nice Question Mar13 comment How long does it take to write a math paper? I don't think it is possible to answer this question. Some papers take days to write, some take years.