Cohomology is the most fundamental global invariant attached to a sheaf. For an l-adic local system L on the complement of a divisor D in a smooth projective variety over an algebraically closed field of characteristic p not equal to l, we will advertise the existence of estimates for the rank of each cohomology spaces of L depending only on local data : the rank of L and the ramification conductors of L at the generic points of D. This is joint work with Haoyu Hu.