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Jan 22, 2013 at 14:20 vote accept Francesco Genovese
Jan 22, 2013 at 14:19 comment added Francesco Genovese I'm checking this example in detail, I'm quite sure it works. I will accept this answer, I think it's the "simplest" one given here. Of course, I would like to thank the other answerers, too: I believe that all examples given here are correct.
Jan 22, 2013 at 0:56 comment added Dag Oskar Madsen Changed the ring after Eric's suggestion.
Jan 22, 2013 at 0:53 history edited Dag Oskar Madsen CC BY-SA 3.0
Changed the ring $R$ after Eric's suggestion; added 22 characters in body
Jan 22, 2013 at 0:28 comment added Dag Oskar Madsen Sure, might be better. I'm used to thinking small $k$-dimension, but here maybe small homological dimension is more relevant :)
Jan 22, 2013 at 0:07 comment added Eric Wofsey If you work instead over a full polynomial ring $k[x,y]$, this gives an example where both $A$ and $B$ are perfect complexes.
Jan 21, 2013 at 23:42 history answered Dag Oskar Madsen CC BY-SA 3.0