I want to know the "cohomological dimension" of a Stein manifold.

I know that:

• for $X$ differential manifold and for every sheaf $F$ of abelian
  groups, I have $H_c^j(X,F)=H^j(X,F)=0$ for $j>\dim_{R}X$ (sheaves and manifold, Kashiwara, Schapira)

• for $Y$ a noetherian scheme of dimension n (or, if it's false, just an algebraic variety over an algebraically closed field $k$) and $F$ a sheaf of group, $H_c^j(X,F)=H^j(X,F)=0$ for $j>\dim Y$.

Does there exist an equivalent result for stein space? Something like: for all sheaf $F$ of $C$-vector spaces in a stein space of complex dimension $d$, $H_c^j(X,F)=H^j(X,F)=0$ for $j>d$?

Thanks for any answer! (and sorry for my English)

I want to know the "cohomological dimension" of a Stein space.

I know that:

• for $X$ differential manifold and for every sheaf $F$ of abelian
  groups, I have $H_c^j(X,F)=H^j(X,F)=0$ for $j>\dim_{R}X$ (sheaves and manifold, Kashiwara, Schapira)

• for $Y$ a noetherian scheme of dimension n (or, if it's false, just an algebraic variety over an algebraically closed field $k$) and $F$ a sheaf of group, $H_c^j(X,F)=H^j(X,F)=0$ for $j>\dim Y$.

Does there exist an equivalent result for stein space? Something like: for all sheaf $F$ of $C$-vector spaces in a stein space of complex dimension $d$, $H_c^j(X,F)=H^j(X,F)=0$ for $j>d$?

Thanks for any answer! (and sorry for my English)

I want to know the "cohomological dimension" of a stein manifold.

I know that: -for $X$ differential manifold and for every sheaf $F$ of abelian groups, I have $H_c^j(X,F)=H^j(X,F)=0$ for $j>dim_{R}X$ (sheaves and manifold, Kashiwara, Schapira)
-for $Y$ a noetherian scheme of dimension n (or, if it's false, just an algebraic variety over an algebraically closed field $k$) and $F$ a sheaf of group, $H_c^j(X,F)=H^j(X,F)=0$ for $j>dim Y$.

Does there exist an equivalent result for stein space? Something like: for all sheaf $F$ of $C$-vector spaces in a stein space of complex dimension $d$, $H_c^j(X,F)=H^j(X,F)=0$ for $j>d$? I don't find this result.

Thanks for any answer! (and sorry for my english)

I want to know the "cohomological dimension" of a Stein manifold.

I know that:

• for $X$ differential manifold and for every sheaf $F$ of abelian
  groups, I have $H_c^j(X,F)=H^j(X,F)=0$ for $j>\dim_{R}X$ (sheaves and manifold, Kashiwara, Schapira)

• for $Y$ a noetherian scheme of dimension n (or, if it's false, just an algebraic variety over an algebraically closed field $k$) and $F$ a sheaf of group, $H_c^j(X,F)=H^j(X,F)=0$ for $j>\dim Y$.

Does there exist an equivalent result for stein space? Something like: for all sheaf $F$ of $C$-vector spaces in a stein space of complex dimension $d$, $H_c^j(X,F)=H^j(X,F)=0$ for $j>d$?

Thanks for any answer! (and sorry for my English)