About: Theorem of absolute purity

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In algebraic geometry, the theorem of absolute (cohomological) purity is an important theorem in the theory of étale cohomology. It states: given * a regular scheme X over some base scheme, * a closed immersion of a regular scheme of pure codimension r, * an integer n that is invertible on the base scheme, * a locally constant étale sheaf with finite stalks and values in , for each integer , the map is bijective, where the map is induced by cup product with .

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  • In algebraic geometry, the theorem of absolute (cohomological) purity is an important theorem in the theory of étale cohomology. It states: given * a regular scheme X over some base scheme, * a closed immersion of a regular scheme of pure codimension r, * an integer n that is invertible on the base scheme, * a locally constant étale sheaf with finite stalks and values in , for each integer , the map is bijective, where the map is induced by cup product with . 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. (en)
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  • In algebraic geometry, the theorem of absolute (cohomological) purity is an important theorem in the theory of étale cohomology. It states: given * a regular scheme X over some base scheme, * a closed immersion of a regular scheme of pure codimension r, * an integer n that is invertible on the base scheme, * a locally constant étale sheaf with finite stalks and values in , for each integer , the map is bijective, where the map is induced by cup product with . (en)
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  • Theorem of absolute purity (en)
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