Constructible étale abelian sheafs on $Spec\ O_\mathbb K$, for number fields $\mathbb K$, satisfy Artin-Verdier duality. Are there known any algebraic schemes or algebraic stacks, other than $Spec\ O_\mathbb K$ and their open subsets, for which (a version of) A-V duality holds?
The motivation for my question is that Artin-Verdier duality is reminiscent of Poincare duality for $3$-dimensional manifolds. Since 3-manifolds can be easily glued of pieces, it is natural to ask about an analog of that construction in which schemes $Spec\ O_\mathbb K$ are spliced together.
In particular, one can construct 3-manifolds is by taking branched covers of other 3-manifolds. Obviously, every field extension $\mathbb K\subset \mathbb L$ defines a branched cover $Spec\ O_\mathbb L\to Spec\ O_\mathbb K,$ but perhaps there is a reasonable notion of branched cover $Y\to Spec\ O_\mathbb K$ in which $Y$ satisfies a version of A-V duality, even though it is not $Spec\ O_\mathbb L$?
