Let $\textbf {X}$ be a noetherian scheme,

$\textbf {M(X)}$ be the categroy of coherent sheaf over the scheme $\textbf {X}$.

We denote $ \textbf {K$_0$(M(X))}$ to be $ \textbf {G$_0$(X)}$.

Now I know that since $\textbf {X}$ is noetherian it has a finite cover by **Spec(A$_i$)** for some $i$ = 1,2,..n. and **A$_i$** for each $i$ is noetherian.

and there is an equivalence between the categories of **M(Spec(A$_i$))** and fintely generated **A$_i$** modules.

I have proved that **G$_0$ (A$_i$$_{red}$)** $\cong $ **G$_0$ (A$_i$)** where **G$_0$ (R)** is **K$_0$(M(R))**;

Notation **M(R)** = finitely generated R module (R -noetherian in this case).

Now Can I say this, that since every open set in the cover of **X** has **G$_0$ (A$_i$$_{red}$)** $\cong $ **G$_0$ (A$_i$)** then

**G$_0$**(X) $\cong$ **G$_0$(X$_{red}$)** .

**So my query is to prove the above mentioned statement does it suffice to prove it for affine noetherian scheme?** As I know that every open affine subset of a noetherian scheme is noetherian.