Hasse-Weil zeta function

A tyoe of L function associated to $X\in {\mathsf{Alg}}{\mathsf{Var}}$ defined over a number field $K$.
Global, so an Euler product of local zeta functions
For $K = {\mathbb{Q}}$ and $V \in {\mathsf{Sch}}_{/ {\operatorname{Spec}{\mathbb{Z}}}} $, reduction $\operatorname{mod}p$ is pulling back:

\begin{align*}\begin{tikzcd} {X\operatorname{mod}p} && X \\ \\ {\operatorname{Spec}{\mathbb{F}}_p} && {\operatorname{Spec}{\mathbb{Z}}} \arrow[from=3-1, to=3-3] \arrow[from=1-3, to=3-3] \arrow[from=1-1, to=3-1] \arrow[from=1-1, to=1-3] \arrow["\lrcorner"{anchor=center, pos=0.125}, draw=none, from=1-1, to=3-3] \end{tikzcd}\end{align*}

Link to Diagram

This works for almost all $p$ and corresponds to reducing the coefficients $\operatorname{mod}p$.