List questions from fibre-product

Published on 30 Jul 2020 - 12:05

110

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Does a fiber product of a group $G$ by itself have $G$ as a subgroup?

Published on 09 Feb 2023 - 18:22

36

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fibre product with a scheme in terms of its glueing data

Published on 28 Mar 2023 - 10:01

110

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How to prove $Spec A_1\times Spec A_2=Spec ( A_1\otimes A_2)$ by a direct way?

Published on 05 Sep 2023 - 16:38

86

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Base change of proper map is proper

Published on 23 Feb 2026 - 4:27

88

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$Gal(LM/K)$ isomorphic to $ \{ (\sigma , \tau) \in Gal(L/K) \times Gal(M/K) : \sigma |_{L \cap M} = \tau |_{L \cap M} \} $

Published on 08 Dec 2023 - 14:13

47

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Exercise about fibre product of varieties

Published on 11 Jan 2024 - 14:42

27

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Extension of a distinguished base in Vakil's notes

Published on 04 Feb 2024 - 14:26

71

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Affine morphisms are stable under base change

Published on 15 Feb 2024 - 16:25

42

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Doubt in the Magic Square

Published on 15 Feb 2024 - 18:29

66

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Is fiber product of $M_s$ , $M_t$ over $M_{st}$ isomorphic to $M$?

Published on 01 Mar 2024 - 16:46

35

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Generation of a projective module by fiber product

Published on 03 Mar 2024 - 0:44

17

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Generalizations of fibre products

Published on 27 Mar 2024 - 14:28

78

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If $f: a \to b$ is representable and $g: b \to c$ is representable, then so is the composition $g\circ f$.

Published on 30 May 2017 - 0:45

42

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$(h_u \times_{\xi, G, a} F)(X) = \{(f, \xi) : x \xrightarrow{f} u, \xi' \in F(X), G(f)(\xi) = a_x(\xi')\}$ using definition of fibre product.

Published on 30 May 2017 - 23:02

List Question

What do the prime ideals of $A \otimes_C B$ look like?

Does a fiber product of a group $G$ by itself have $G$ as a subgroup?

fibre product with a scheme in terms of its glueing data

How to prove $Spec A_1\times Spec A_2=Spec ( A_1\otimes A_2)$ by a direct way?

Base change of proper map is proper

$Gal(LM/K)$ isomorphic to $ \{ (\sigma , \tau) \in Gal(L/K) \times Gal(M/K) : \sigma |_{L \cap M} = \tau |_{L \cap M} \} $

Exercise about fibre product of varieties

Extension of a distinguished base in Vakil's notes

Affine morphisms are stable under base change

Doubt in the Magic Square

Is fiber product of $M_s$ , $M_t$ over $M_{st}$ isomorphic to $M$?

Generation of a projective module by fiber product

Generalizations of fibre products

If $f: a \to b$ is representable and $g: b \to c$ is representable, then so is the composition $g\circ f$.

$(h_u \times_{\xi, G, a} F)(X) = \{(f, \xi) : x \xrightarrow{f} u, \xi' \in F(X), G(f)(\xi) = a_x(\xi')\}$ using definition of fibre product.

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