List questions from flatness

Published on 12 Apr 2026 - 3:10

113

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Flat affine group scheme $G$ over $\mathbb{Z}$ arises from embedding generic fiber $G_{\mathbb{Q}}$ into $GL_{n,\mathbb{Q}}$.

Published on 15 Apr 2026 - 12:26

229

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Restriction of a flat/smooth morphism with nice properties

Published on 12 Apr 2026 - 0:57

66

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When $P\otimes_R M \to R \otimes_R M$ is injective for every (finitely generated) prime ideals $P$ of $R$?

Published on 16 Apr 2026 - 12:28

61

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The dimension of stalks for flat morphisms

Published on 15 Apr 2026 - 22:03

359

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$K(X)$ is not faithfully flat $K[X]$ module.

Published on 15 Apr 2026 - 19:11

113

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Is $\Bbb Z[i]$ flat as $\Bbb Z[2i]$-module?

Published on 13 Apr 2026 - 10:35

181

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about torsion and flat module

Published on 16 Apr 2026 - 4:26

84

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about flat $R$-modules with different conditions

Published on 10 Apr 2026 - 16:17

532

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Integral Closure Flat

Published on 10 Apr 2026 - 10:02

67

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Faithfully Flat imply $aA = aB \cap A$

Published on 12 Apr 2026 - 3:21

359

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When does a quasifinite surjective flat morphism have constant fiber multiplicity near a point?

Published on 11 Apr 2026 - 22:30

130

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Is constancy of fiber degree analytic-local on the source in a finite flat family?

Published on 10 Apr 2026 - 16:18

288

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$\forall\, 0\to N\to M\to F\to 0 $ exact, $\forall R$-module $E$, $F$ is flat $\implies 0 \to N\otimes E\to M\otimes E\to F\otimes E \to0$ is exact.

Published on 16 Apr 2026 - 14:44

467

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tensoring with flat module factors the kernel

Published on 10 Apr 2026 - 2:13

List Question

Absolutely Flat Ring

Flat affine group scheme $G$ over $\mathbb{Z}$ arises from embedding generic fiber $G_{\mathbb{Q}}$ into $GL_{n,\mathbb{Q}}$.

Restriction of a flat/smooth morphism with nice properties

When $P\otimes_R M \to R \otimes_R M$ is injective for every (finitely generated) prime ideals $P$ of $R$?

The dimension of stalks for flat morphisms

$K(X)$ is not faithfully flat $K[X]$ module.

Is $\Bbb Z[i]$ flat as $\Bbb Z[2i]$-module?

about torsion and flat module

about flat $R$-modules with different conditions

Integral Closure Flat

Faithfully Flat imply $aA = aB \cap A$

When does a quasifinite surjective flat morphism have constant fiber multiplicity near a point?

Is constancy of fiber degree analytic-local on the source in a finite flat family?

$\forall\, 0\to N\to M\to F\to 0 $ exact, $\forall R$-module $E$, $F$ is flat $\implies 0 \to N\otimes E\to M\otimes E\to F\otimes E \to0$ is exact.

tensoring with flat module factors the kernel

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