1
$\begingroup$

let $f:X\to S$ be a proper morphism of schemes with $S=Spec(A)$ affine. Consider $F$ a constructible sheaf on $X$. I am interested to know for which ring $B$ with morphism $Spec(B)\to Spec(A)$ is it true that the morphism

$(f_{*}F)\otimes B \to H^0(X_B, F_B)$

is an isomorphism.

I am interested expecially in the case $Spec(B)\to Spec(A)$ étale, or $B=k(p)$ the residue field of a point $p\in Spec(A)$.

Thanks

  • 0
    @Harry yes!I don't understand why one should have the isomorphism $(f_{*}F)\otimes k(p)\cong (f_{*}F)_{p}$, and $(f_{*}F)\otimes B\cong (f_{*}F)_{Spec(B)}$. Is it just a definition?2012-07-11

0 Answers 0