I work in derived category $D^b(X)$ of constructible sheaves on a reasonable space $X$. Let $j\colon U\to X$ be an open inclusion and $i\colon Y\to X$ the closed complement. Let $M,N\in D^b(X)$ and ...
I would like to understand the theory of pure complexes of (etale?) sheaves (of geometric origin?). In particular, I would like to understand which conditions are realy necessary in (part 1 of) ...