How does isomorphism of schemes induce maps on cohomology groups











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Let $f:X to X$ be an isomorphism of schemes. Let $mathcal{F}$ be sheaf of abelian groups on $X$.



When does $f$ induces a map $H^i(X, mathcal{F}) to H^i(X, mathcal{F})$?



I've seen similar statements at many places at least certain types of $mathcal{F}$ but never seen a proper explanation of how such a map exists?






algebraic-geometry sheaf-theory sheaf-cohomology







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    up vote
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    down vote

    favorite
    1












    Let $f:X to X$ be an isomorphism of schemes. Let $mathcal{F}$ be sheaf of abelian groups on $X$.



    When does $f$ induces a map $H^i(X, mathcal{F}) to H^i(X, mathcal{F})$?



    I've seen similar statements at many places at least certain types of $mathcal{F}$ but never seen a proper explanation of how such a map exists?






    algebraic-geometry sheaf-theory sheaf-cohomology







    share|cite|improve this question
























      up vote
      0
      down vote

      favorite
      1









      up vote
      0
      down vote

      favorite
      1






      1





      Let $f:X to X$ be an isomorphism of schemes. Let $mathcal{F}$ be sheaf of abelian groups on $X$.



      When does $f$ induces a map $H^i(X, mathcal{F}) to H^i(X, mathcal{F})$?



      I've seen similar statements at many places at least certain types of $mathcal{F}$ but never seen a proper explanation of how such a map exists?






      algebraic-geometry sheaf-theory sheaf-cohomology







      share|cite|improve this question













      Let $f:X to X$ be an isomorphism of schemes. Let $mathcal{F}$ be sheaf of abelian groups on $X$.



      When does $f$ induces a map $H^i(X, mathcal{F}) to H^i(X, mathcal{F})$?



      I've seen similar statements at many places at least certain types of $mathcal{F}$ but never seen a proper explanation of how such a map exists?






      algebraic-geometry sheaf-theory sheaf-cohomology




      algebraic-geometry sheaf-theory sheaf-cohomology






      share|cite|improve this question













      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










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