limit of étale cohomology of representable sheaf - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-18T22:06:03Z http://mathoverflow.net/feeds/question/82092 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/82092/limit-of-etale-cohomology-of-representable-sheaf limit of étale cohomology of representable sheaf norondion 2011-11-28T15:23:42Z 2011-11-28T15:23:42Z <p>Let $\mathcal{F}$ be a representable sheaf on a smooth irreducible scheme $X$ and $Y \hookrightarrow X$ be an integral reduced closed subscheme with generic point $\eta_Y$. How does $H^n_Y(X,\mathcal{F})$ compare to $H^n_{\eta_Y}( \mathcal{O}_{X,\eta_Y},\mathcal{F})$ (étale cohomology), i.e. is there an injective map in some direction? I want to apply excision, but this forces me to leave $Y$ fixed; and I also don't see how to apply Milne, Étale cohomology, Lemma III.1.16 for the same reason.</p>