let k be a perfect field of characteristic p, and let gal(k) denote the absolute galois group of k. by a classical result of katz, the category of finite-dimensional $f_p-vector spaces$ with an action of gal(k) is equivalent to the category of finite-dimensional vector spaces over k with a frobenius-semilinear automorphism. in this talk, i'll discuss some joint work with bhargav bhatt which generalizes katz's result, replacing the field k by an arbitrary $f_p-scheme x$. in this case, there is a correspondence relating p-torsion etale sheaves on x to quasi-coherent sheaves on x equipped with a frobenius-semilinear automorphism, which can be viewed as a ``mod p'' version of the riemann-hilbert correspondence for complex algebraic varieties.