List questions from arithmetic-geometry

Published on 14 May 2023 - 0:25

80

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Is Mordell conjecture true for local field?

Published on 17 May 2023 - 2:46

102

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Definition of principal homogeneous space for elliptic curves

Published on 25 Mar 2026 - 14:34

31

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Action of complex conjugation on abelian surfaces with complex multiplication

Published on 25 Mar 2026 - 3:01

116

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Is there a plane curve of degree $d$ with more than $d^2$ rational points?

Published on 18 May 2023 - 13:48

91

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Voight Quaternion Algebras proof of Lemma 42.2.7

Published on 30 May 2023 - 17:59

157

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Rank of elliptic curve over $\Bbb{Q}(2^{1/3})$

Published on 03 Jun 2023 - 6:00

136

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How is the field extension finite

Published on 23 Feb 2026 - 2:42

55

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Why $[E(K_q) : E_0(K_q)] ≤ 4$ and $E_0(K_q)$ is divisible by $2$ implies $E(K_q)[2^∞] = E[2]$?

Published on 26 Mar 2026 - 4:30

52

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Why does the map induce an injection of function fields

Published on 15 Jun 2023 - 7:35

166

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Definition of Chern Class

Published on 15 Jun 2023 - 13:52

166

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Other counterexample of local global principle except for $2y^2=x^4-17$ in Tate-Shafarevich group

Published on 18 Jun 2023 - 15:44

169

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Existence of non-degenerate alternating pairing $ \psi : A \times A \to \mathbb{Q}/\mathbb{Z} $ and perfect square cardinality

Published on 26 Jun 2023 - 6:06

40

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When are mirror-image modular curves isomorphic to each other?

Published on 27 Jun 2023 - 6:16

97

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Rational maps from $\mathbb{P}^{1}$ to $\mathbb{P}^{1}$

Published on 28 Jun 2023 - 14:37

List Question

Hasse-Weil Theorem Reference

Is Mordell conjecture true for local field?

Definition of principal homogeneous space for elliptic curves

Action of complex conjugation on abelian surfaces with complex multiplication

Is there a plane curve of degree $d$ with more than $d^2$ rational points?

Voight Quaternion Algebras proof of Lemma 42.2.7

Rank of elliptic curve over $\Bbb{Q}(2^{1/3})$

How is the field extension finite

Why $[E(K_q) : E_0(K_q)] ≤ 4$ and $E_0(K_q)$ is divisible by $2$ implies $E(K_q)[2^∞] = E[2]$?

Why does the map induce an injection of function fields

Definition of Chern Class

Other counterexample of local global principle except for $2y^2=x^4-17$ in Tate-Shafarevich group

Existence of non-degenerate alternating pairing $ \psi : A \times A \to \mathbb{Q}/\mathbb{Z} $ and perfect square cardinality

When are mirror-image modular curves isomorphic to each other?

Rational maps from $\mathbb{P}^{1}$ to $\mathbb{P}^{1}$

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