Hi!

I am looking for basic references about infinite dimensional algebraic geometry, in particular about the $\textrm{Proj}$ of an infinite dimensional graded commutative algebra.

I have a specific problem as well. I have two projective systems of finite dimensional $\mathbb{C}$-algebras, $A_n$ and $B_n$ ($n$ runs overt the positive integers), both projective limits are infinite dimensional. I have surjective (with a big kernel!) maps $T_n$ from $A_n$ to $B_n$ which are compatible with the projective limit. Moreover, the map $T_{\infty}$ is an isomorphism. Does this mean that the varieties "$\textrm{Proj }A_{\infty}$" and "$\textrm{Proj }B_{\infty}$" are isomorphic?