Quantitative sheaf theory

We introduce a notion of complexity complex ℓ \ell -adic sheaves on quasi-projective variety and prove that the six operations are “continuous”, in sense output is bounded solely terms input sheaves. A key feature it provides bounds for sum Betti numbers that, many interesting cases, can be made uniform characteristic base field. As an illustration, we discuss few simple applications to horizontal equidistribution results exponential sums over finite fields.