# Fibre product of complex analytic spaces - reference request

Let $X$ and $Y$ be two possibly non reduced analytic spaces over a third analytic space $S$. I have not been able to find a reference where the fibre product $X\times_S Y$ is constructed !!!! Any help would be appreciated.

My guess is that the topological space is just the fibre product of topological spaces; and, at least when $S$ is a point, the structure sheaf is the sheaf associated to the pre-sheaf which on $U\times V$ is $\mathcal{O}_X(U)\otimes_{\mathbb{C}}\mathcal{O}_Y(V)$.

I really would like to have a reference!

• The fiber product is defined for instance in the book "Several Complex Variables IV: Algebraic Aspects of Complex Analysis", page 116.
– HYL
Apr 21, 2017 at 9:23
• Thanks! This is what I was looking for. You are welcome to write it as an answer Apr 21, 2017 at 9:28