As the question title suggests, what is the role cohomology of coherent sheaves plays for SGA 4.5, étale cohomology? Why are they so important for the construction and establishing properties of étale cohomology? What are some of the main essences and theorems of the cohomology of coherent sheaves that are exploited or get "carried over", in some sense?
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Role of cohomology of coherent sheaves in SGA 4.5, étale cohomology
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