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!



Fibre product of complex analytic spaces - reference request
Apart from the reference given in the comment, you can also find a proof of the existence of the fiber product in Fischer's "Complex Analytic Geometry", Corollary 0.32.


For direct products, a more straightforward construction can be found in Grauert and Remmert's "Coherent Analytic sheaves", Chapter 1.3. As they pointed out, their method avoids analytic tensor products of the structure sheaves.


