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

Abstract

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 to be perfect. Let $X$ be a separated $k$-scheme of finite type and $Y$ be an open subscheme of $X$. We construct the category $F\text{-}D ^\mathrm{b}_\mathrm{ovhol} (\mathcal{D} ^\dag_{(Y,X)/K})$ of overholonomy type over $(Y,X)/K$. We check that these categories satisfy a formalism of Grothendieck's six operations.