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In algebraic geometry, the theorem of absolute purity is an important theorem in the theory of étale cohomology. It states: given
for each integer m ≥ 0 {\displaystyle m\geq 0} , the map
is bijective, where the map is induced by cup product with c r {\displaystyle c_{r}}.
The theorem was introduced in SGA 5 Exposé I, § 3.1.4. as an open problem. Later, Thomason proved it for large n and Gabber in general.
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