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Let $\mathcal{V}$ be a complete discrete valued ring of mixed characteristic$(0,p)$, $K$ its field of fractions, $k$ its residue field which is supposed tobe perfect. Let $X$ be a separated $k$-scheme of finite type and $Y$ be an opensubscheme of $X$. We construct the category $F\text{-}D^\mathrm{b}_\mathrm{ovhol} (\mathcal{D} ^\dag_{(Y,X)/K})$ of overholonomy typeover $(Y,X)/K$. We check that these categories satisfy a formalism ofGrothendieck's six operations.

The formalism of Grothendieck's six operations in p-adic cohomologies