Let $X$ be a complex algebraic variety and consider the category $P(X)$ of perverse sheaves of complex vector spaces.

Let $f:X\rightarrow \mathbb C$ be a regular function, $Z$ its zero set and $U$ its complement.

A glueing data consists of a tuple $({\cal F}_U,{\cal F}_Z, u,v)$, where ${\cal F}_U$ and ${\cal F}_Z$ are perverse sheaves on $U$ and $Z$ and $u,v$ are maps going between the nearby cycles $\psi({\cal F}_U)$ and ${\cal F}_Z$ such that $u\circ v=1-T$, where $T$ is the monodromy operator on $\psi({\cal F}_U)$. These glueing data form a category $Glue(U,Z)$ in an obvious way.

Now it is known, that $Glue(U,Z)$ is equivalent to $P(X)$. My question is, does this still hold if we take instead of perverse sheaves of complex vectorspaces perverse sheaves of say abelian groups? I am also interested in the variant where one takes unipotent nearby cycles.

I suspect the answer is yes, because if I checked correctly the glueing construction in "Tilting exercises" works over the integers. On the other hand I must admit that I neither understand the details of the above glueing construction very well nor its precise relation to the one in "Tilting exercises".