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May 27, 2011 at 21:23 comment added Thomas Nevins Ah, thanks a lot for clarifying this (even though it wasn't anything unclear about your original post, just my somewhat careless reading)...I tend to think about this through the lens of Neeman (so the natural thing is the right adjoint to $\mathbb{R}f_*$, in which case quasicompact quasiseparated is plenty to ensure that the qcoh derived category is compactly generated etc.). Though of course you're right that the original post is rather about what e.g. Lipman would call the "twisted inverse image," i.e. the "classical" $f^!$, and its adjoint.
May 27, 2011 at 20:19 history edited Anatoly Preygel CC BY-SA 3.0
Clarifications..
May 27, 2011 at 18:20 history answered Anatoly Preygel CC BY-SA 3.0