given functors $F,G$, left exact, with as good properties as you want we have a spectral sequence $R^p F\circ R^q G$ abutting to $R^{p+q}(F\circ G)$. I am looking for an analogous for a "mixed version" in te following case: $F$ left exact and $G$ right exact. What appens to $L^pG\circ R^q F$?
Grothendieck spectral sequence
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algebraic-geometry
commutative-algebra
homological-algebra