Étale cohomology is a type of cohomology theory in algebraic geometry that extends the notion of sheaf cohomology to the étale topology, which is a way of looking at spaces in a more flexible manner. It provides powerful tools for studying the properties of algebraic varieties and their functions, especially over fields that may not be algebraically closed. This theory connects deeply with aspects like the fundamental group of schemes and can be used to prove results related to the structure of algebraic varieties, particularly in the context of Hilbert's Nullstellensatz.
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