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# NonzeroNon-zero sheaf cohomology

Let R denote the real line with its usual topology. Does there exist a sheaf F of abelian groups on R whose second cohomology group H^2(R,F) is non- zeronon-zero? What about H^j(R,F) for integers j>=2 ?

(Here cohomology means derived functor cohomology as in,sayin, say, Hartshorne or EGA. Anyway this cohomology coincides with Cech cohomology since R is paracompact.)

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Is

Let R denote the real line with its usual topology. Does there exist a sheaf F of abelian groups on R whose second (or higher) cohomology group H^2(R,F) is non-zeronon- zero? What about H^j(R,F) for integers j>=2 ?

(Here cohomology means derived functor cohomology as in,say, Hartshorne or EGA. Anyway this cohomology coincides with Cech cohomology since R is paracompact.)

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# Non zero sheaf cohomology

Is there a sheaf of abelian groups on R whose second (or higher) cohomology group is non-zero?