Questions tagged [fibre-products]

Let's work over $\mathbb{C}$. Consider the following commutative diagram \begin{array}{llllllllllll} E_1& \xrightarrow{f} &E_2\\ \downarrow{\pi} &&\downarrow{\pi}\\ P_1 & \...

I do not understand one argument in the proof of Proposition 0.4.5.4. in the new version by Springer of EGA I. When proving that the functor $F$ is representable by $(X, \xi)$, where we obtained $X$ ...

Harold asks what conditions on $f:M\to L$ and $g:N\to L$, both smooth maps of smooth manifolds, ensures the existence of the fibre product $M \times_L N$.

Usually, the most general condition for fiber product of manifolds (or vector bundles) to exist is that we require the images cleanly intersects. See e.g. When do fibre products of smooth manifolds ...

This question is, in a way, a follow-up of this earlier question of mine. Background Let $A$, $B$ and $F$ be finite groups and let $\alpha: A \to F$ and $\beta: B \to F$ be surjective homomorphisms. ...

Let $X$ (resp. $Y$) be the affine $k$-scheme defined by the ideal $I$ (resp. $J$) in the polynomial ring $k[x_1,...x_n]$ (resp. $k[y_1,...,y_m]$). Let $Z$ be the affine scheme defined by the ideal $L$...