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For a scheme $X$ separated and of finite type over an excellent regularscheme $S$, we define wildly compatible systems of constructible sheaves ofmodules over finite fields on $X$ for certain vector spaces $V$. The mainresult is that for $\dim S \leq 1$, wildly compatible systems are preserved byGrothendieck's six operations and Verdier's duality. Finally, for a smoothintegral scheme $X$ over a finite field, we prove that all $\ell$-adiccompatible systems gives wildly compatible systems.

Wildly Compatible Systems and Six Operations