model theory - Cohomology Theories on The Stone Space of Complete n-types

I can not really inform you about this since I don't know, but I can point you to some notes of Angus Macintyre,
http://modular.math.washington.edu/swc/notes/files/03MacintyreNotes.pdf

Here are some excerpts:

"For me personally, the main surprise arising from the discovery of ACFA
was how much there was to be done in terms of a model-theoretic reaction
to the development of etale cohomology and its relatives."

"Again, in a different direction, one begins to see cohomological ideas coming
up all over applied model theory, for example in o-minimality."

I hope that you find this useful.