List questions from flatness

Published on 21 Nov 2023 - 23:15

90

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Show the problem of flat base change is local on the source and target

Published on 13 Dec 2023 - 9:40

64

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$\mathbb Z[\xi_{2n}]$ is a pid

Published on 13 Dec 2023 - 23:12

81

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Free module over local ring $R$.

Published on 25 Mar 2026 - 21:44

88

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Miracle flatness on Wikipedia's "Cohen--Macaulay ring"

Published on 08 Jan 2024 - 12:21

49

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Is projective morphism over a discrete valuation ring always flat?

Published on 25 Mar 2026 - 13:59

93

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[Cor 5.3.24 in Qing Liu]If $X$ is a projective scheme over a DVR $A$, then any coherent sheaf of ideal of $\mathcal{O}_X$ is flat over $A$?

Published on 25 Mar 2026 - 13:58

85

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Interpretation of $B\otimes M$ when $B\subset A$

Published on 11 Jan 2024 - 14:29

44

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"Explicit" showing of non-flatness for a fractional ideal

Published on 29 Jan 2024 - 17:35

38

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If $M$ is a flat $R-$module and $I$ is an ideal of $R$, why is $I\otimes_R M$ isomorphic to $IM$?

Published on 17 Feb 2024 - 4:50

57

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Pullback of a flat module is flat

Published on 09 Mar 2024 - 20:31

71

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A Criterion for Faithfully Flatness via Intersection Property

Published on 15 Mar 2024 - 16:17

51

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Is the quotient of an infinite product of fields by the direct sum injective?

Published on 22 Mar 2024 - 16:10

25

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Flat base change preserves the non-degeneracy (Proposition 9.2 in Commutative Algebra, Matsumura)

Published on 26 Mar 2024 - 22:00

1.3k

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Exact sequence with flat module tensored by module stays exact

Published on 17 Jan 2015 - 12:27

List Question

Prove that the polynomial ring $R[x]$ is a flat $R$-module.

Show the problem of flat base change is local on the source and target

$\mathbb Z[\xi_{2n}]$ is a pid

Free module over local ring $R$.

Miracle flatness on Wikipedia's "Cohen--Macaulay ring"

Is projective morphism over a discrete valuation ring always flat?

[Cor 5.3.24 in Qing Liu]If $X$ is a projective scheme over a DVR $A$, then any coherent sheaf of ideal of $\mathcal{O}_X$ is flat over $A$?

Interpretation of $B\otimes M$ when $B\subset A$

"Explicit" showing of non-flatness for a fractional ideal

If $M$ is a flat $R-$module and $I$ is an ideal of $R$, why is $I\otimes_R M$ isomorphic to $IM$?

Pullback of a flat module is flat

A Criterion for Faithfully Flatness via Intersection Property

Is the quotient of an infinite product of fields by the direct sum injective?

Flat base change preserves the non-degeneracy (Proposition 9.2 in Commutative Algebra, Matsumura)

Exact sequence with flat module tensored by module stays exact

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