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The purpose of this note is to show that if $char \\, k =p$ then there are very simple examples of such functors. Namely, for a smooth projective $Y$ over $\\mathbb Z_p$ with the special fiber $i: X\\hookrightarrow Y$, we consider the functor $L i^* \\circ i_*: D^b(X) \\to D^b(X)$ from the derived categories of coherent sheaves on $X$ to itself. 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