Theory of weights in p-adic cohomology

Let $k$ be a finite field of characteristic $p>0$. We construct a theory of weights for overholonomic complexes of arithmetic ${\cal D}$-modules with Frobenius structure on varieties over $k$. The notion of weight behave like Deligne's one in the $\ell$-adic framework: first, the six operations preserve weights, and secondly, the intermediate extension of an immersion preserves pure complexes and weights.