List questions from transcendence-degree

Published on 22 Feb 2026 - 21:01

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Dimension of scheme of finite type over a field under base change (Hartshorne Ex. II.3.20)

Published on 03 Feb 2018 - 15:45

158

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Show that $[k(t): k(t^4 + t) ] = 4$

Published on 06 Apr 2018 - 16:19

176

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Lüroth's theorem for transcendence degree two

Published on 06 May 2018 - 1:28

118

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Non-injective polynomial map $\mathbb{R}^2 \to \mathbb{R}^2$, injective on lines

Published on 07 May 2018 - 0:56

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Are all transcendental numbers a zero of a power series?

Published on 08 Sep 2018 - 17:00

343

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If $E$ is algebraic extension field of $F$, then also $E(x)$ is algebraic extension of $F(x)$?

Published on 28 Sep 2018 - 8:08

160

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Can you determine the transcendence degree of an algebra by looking at a generating set?

Published on 06 Oct 2018 - 15:38

56

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For $C,D \in \mathbb{Z}[x,y]$: $\operatorname{Jac}(C,D)=0$ if and only if $C$ and $D$ are algebraically dependent over $\mathbb{Z}$?

Published on 31 Oct 2018 - 12:41

634

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transcendence basis of field extensions of $\mathbb{Q}$

Published on 27 Dec 2018 - 18:51

349

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Is every affine variety birational to affine space?

Published on 19 Feb 2019 - 20:33

1.1k

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Dimension of product of varieties

Published on 10 Mar 2019 - 10:45

291

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Degeneration of transcendence degree in polynomial rings

Published on 15 Jul 2019 - 1:17

116

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What would be some implications of Schanuel's conjecture being proven wrong?

Published on 21 Jul 2019 - 18:57

643

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Proof verification: transcendence degree additive in towers

Published on 11 Nov 2019 - 12:48

List Question

A field extension of degree $\leq 2$

Dimension of scheme of finite type over a field under base change (Hartshorne Ex. II.3.20)

Show that $[k(t): k(t^4 + t) ] = 4$

Lüroth's theorem for transcendence degree two

Non-injective polynomial map $\mathbb{R}^2 \to \mathbb{R}^2$, injective on lines

Are all transcendental numbers a zero of a power series?

If $E$ is algebraic extension field of $F$, then also $E(x)$ is algebraic extension of $F(x)$?

Can you determine the transcendence degree of an algebra by looking at a generating set?

For $C,D \in \mathbb{Z}[x,y]$: $\operatorname{Jac}(C,D)=0$ if and only if $C$ and $D$ are algebraically dependent over $\mathbb{Z}$?

transcendence basis of field extensions of $\mathbb{Q}$

Is every affine variety birational to affine space?

Dimension of product of varieties

Degeneration of transcendence degree in polynomial rings

What would be some implications of Schanuel's conjecture being proven wrong?

Proof verification: transcendence degree additive in towers

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