List questions from arithmetic-geometry

Published on 12 Dec 2023 - 14:37

74

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Does there exist an elliptic curve $E/\Bbb{Q}$ such that for all quadratic number field $K$, $rank(E/K)=rank(E/\Bbb{Q})$?

Published on 12 Dec 2023 - 17:11

151

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Blowing up along a point in the special fiber

Published on 26 Dec 2023 - 22:19

160

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Image of trace of Tate-Shafarevich group of elliptic curves become arbitrary large?

Published on 31 Dec 2023 - 15:49

50

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How Galois group act on $H^1(G_L,E)$?

Published on 27 Mar 2026 - 4:17

62

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Definition of Tate-Shafarevich group up to isomorphism of elliptic curves

Published on 27 Mar 2026 - 4:21

53

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Néron–Tate height with respect to a positive divisor

Published on 26 Mar 2026 - 9:16

25

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Subvariety hitting every residue disk

Published on 10 Jan 2024 - 11:32

73

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Addition of $n$ points on elliptic curves over a finite field

Published on 12 Jan 2024 - 18:50

105

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Regular schemes (related to quadratic rings)

Published on 20 Jan 2024 - 0:47

90

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$ \mathbb{Q}_p $-admissible p-adic representaion

Published on 25 Mar 2026 - 17:36

82

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Using Hurwitz's formula, about $\mathbb{F}_p$-rational points

Published on 21 Jan 2024 - 23:03

64

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Why is the Function Field of the Modular Curve $X(N)$ defined over $\mathbb{Q}(\mu_n)$?

Published on 25 Mar 2026 - 7:48

177

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Example of an elliptic curve which is not defined over $\Bbb{Q}$

Published on 28 Jan 2024 - 8:42

42

Views

A nice description for $t^{k-1}B_{cr}^+/t^kB_{cr}^+$?

Published on 26 Mar 2026 - 16:26

List Question

Sign of square free integer which makes elliptic curves rank $0$

Does there exist an elliptic curve $E/\Bbb{Q}$ such that for all quadratic number field $K$, $rank(E/K)=rank(E/\Bbb{Q})$?

Blowing up along a point in the special fiber

Image of trace of Tate-Shafarevich group of elliptic curves become arbitrary large?

How Galois group act on $H^1(G_L,E)$?

Definition of Tate-Shafarevich group up to isomorphism of elliptic curves

Néron–Tate height with respect to a positive divisor

Subvariety hitting every residue disk

Addition of $n$ points on elliptic curves over a finite field

Regular schemes (related to quadratic rings)

$ \mathbb{Q}_p $-admissible p-adic representaion

Using Hurwitz's formula, about $\mathbb{F}_p$-rational points

Why is the Function Field of the Modular Curve $X(N)$ defined over $\mathbb{Q}(\mu_n)$?

Example of an elliptic curve which is not defined over $\Bbb{Q}$

A nice description for $t^{k-1}B_{cr}^+/t^kB_{cr}^+$?

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