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Questions tagged [fibre-products]

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Ramification divisor with base change

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 & \...
Sheng Meng's user avatar
4 votes
0 answers

EGA I (Springer), Proposition [closed]

I do not understand one argument in the proof of Proposition in the new version by Springer of EGA I. When proving that the functor $F$ is representable by $(X, \xi)$, where we obtained $X$ ...
Daniel W.'s user avatar
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2 votes
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Non-clean fiber products

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 ...
Songhao Li's user avatar
4 votes
2 answers

Isomorphism type of fibered products of groups

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. ...
José Figueroa-O'Farrill's user avatar
1 vote
1 answer

Expressing fiber product of affines via an ideal

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 $L$...
Qfwfq's user avatar
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17 votes
2 answers

When do fibre products of smooth manifolds exist?

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 $M \times_L N$.
20 questions's user avatar
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