Character Sums, Weights, and Cohomology

Question

I know, vaguely, that certain bounds for character sums over finite fields can be determined by looking at weights and the dimensions of certain compactly supported cohomology groups. However, I've never seen this spelled out explicitly and have been searching in vain for a source that does so.

To be somewhat more explicit, we can obtain something like

$$\sum_{x \in \mathbb{F}_{p}} \chi(f(x)) \leq C \cdot p^{d/2} $$

for $\chi$ a nontrivial multiplicative character. I've been told C is the dimension of a certain cohomology group and d is a weight. Anyone know a place where this is made explicit?

Answer 1

Terence Tao recently wrote a blog post that seems to answer this question.