Gauges and $p$-torsion sheaves in characteristic $p$

Let $k$ be a perfect field of characteristic $p$. $\varphi$-gauges over $k$ are, in an appropriate sense, finite sub quotients of $F$-isocrystals. I'll explain how one can associate to such a $\varphi$-gauge a $p$-torsion sheaf over $k$ for a suitable topology. This construction which is a part of a joint work with Uwe Jannsen extends the construction of the finite and flat commutative group scheme associated to a Dieudonné module. The $Q_p$ sheaves we get by passing to the limit are linked to natural objects of $p$-adic Hodge theory and of perfectoid spaces.