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Jun 20, 2019 at 22:08 comment added user20948 @ARockandaHardPlace By the way, I want to point out that this argument also generalizes to the case where $L_{B/A}^{\mathrm{alg}}\simeq0$. The point is that, $S\otimes_RS$ in question is just the Hochshild (or Shukla) homology $\operatorname{HH}(B/A)$, but this is $B$ if the cotangent complex vanishes, because of the HKR filtration.
Dec 30, 2017 at 19:07 comment added A Rock and a Hard Place Thanks, that's just what I was after! It was fact 2) that I was missing before, so thank you for teaching it to me!
Dec 30, 2017 at 19:04 vote accept A Rock and a Hard Place
Dec 30, 2017 at 14:29 history answered user117273 CC BY-SA 3.0