# Is flatness condition for proper base change actually needed?

In his 1988 Paper on Resolutions of Unbounded Complexes, Spaltenstein proves that $$Lg^*Rf_! \cong RF_! LG^*$$ where $$\require{AMScd}$$ $$\begin{CD} A @>F>> B\\ @V G V V @VV g V\\ C @>>f> D \end{CD}$$ is a cartesian square of ringed spaces. He requires an additional finiteness condition for the fibres of $$f$$, and (and this is my question) that $$g$$ is flat.

Since $$g$$ is flat so is $$G$$, and there is no actual left derived functor. Is there a known example showing that the statement is false without the flatness assumption? Are there newer sources than stuff from the 80s?

• The book "Categories and Sheaves" by Kashiwara and Schapira contains quite a bit on the unbounded derived category, but as far as I remember they do not treat any base change formulas. For more there might be something on the Stacks project. – asdq Jul 4 at 12:30