This book makes a systematic study of the relations between the étale
cohomology of a scheme and the orderings of its residue fields. A major
result is that in high degrees, étale cohomology is cohomology of the
real spectrum. It also contains new contributions in group cohomology
and in topos theory. It is of interest to graduate students and
researchers who work in algebraic geometry (not only real) and have some
familiarity with the basics of étale cohomology and Grothendieck sites.
Independently, it is of interest to people working in the cohomology
theory of groups or in topos theory.