List questions from arithmetic-geometry

Published on 18 Dec 2021 - 6:46

162

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Translation of Loic Merel's Paper on Bounds for Elliptic Curves

Published on 26 Mar 2026 - 4:36

56

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What is an isomorphism between $L:aX+bY=Z$ and $\Bbb P^1_K$?

Published on 26 Mar 2026 - 17:36

343

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$p$-adic valuation on algebraic numbers

Published on 29 Mar 2026 - 4:01

102

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The affine scheme Spec $\mathcal{O}_K$ is a curve over F1 too?

Published on 18 Jan 2022 - 17:56

76

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Let $C$ and $C'$ be algebraic (smooth) curves.If morphism $φ:C→C'$ satisfies the condition that $＃φ^{-1}(Q)＝1$ for all $Q∈C'$, why $φ$ is isomorphism?

Published on 24 Jan 2022 - 15:14

149

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Morphism between algebraic (smooth) curves of degree 1 is an isomorphism. Does the converse holds?

Published on 27 Mar 2026 - 17:04

93

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Injection from $WC(E/K)$ to $H^1(G_K,E)$ from Silverman's 'the arithmetic of elliptic curves'

Published on 26 Jan 2022 - 11:52

335

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Decomposition of the regular representation of $S_3$ into irreducible ones.

Published on 04 Feb 2022 - 16:34

150

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What is the needed background to study Euler system?

Published on 11 Feb 2022 - 16:27

534

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Isogenous elliptic curves with the same j-invariant are isomorphic

Published on 13 Feb 2022 - 20:01

65

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Induced map on jacobians of curves of genus one

Published on 14 Feb 2022 - 7:39

165

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CM points on Shimura curves

Published on 25 Mar 2026 - 11:09

136

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Relation between Petersson inner product and cup product

Published on 12 Mar 2022 - 5:33

60

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Quotient of algebraic curve

Published on 30 Mar 2022 - 14:29

List Question

Dense rational points of an elliptic curve

Translation of Loic Merel's Paper on Bounds for Elliptic Curves

What is an isomorphism between $L:aX+bY=Z$ and $\Bbb P^1_K$?

$p$-adic valuation on algebraic numbers

The affine scheme Spec $\mathcal{O}_K$ is a curve over F1 too?

Let $C$ and $C'$ be algebraic (smooth) curves.If morphism $φ:C→C'$ satisfies the condition that $＃φ^{-1}(Q)＝1$ for all $Q∈C'$, why $φ$ is isomorphism?

Morphism between algebraic (smooth) curves of degree 1 is an isomorphism. Does the converse holds?

Injection from $WC(E/K)$ to $H^1(G_K,E)$ from Silverman's 'the arithmetic of elliptic curves'

Decomposition of the regular representation of $S_3$ into irreducible ones.

What is the needed background to study Euler system?

Isogenous elliptic curves with the same j-invariant are isomorphic

Induced map on jacobians of curves of genus one

CM points on Shimura curves

Relation between Petersson inner product and cup product

Quotient of algebraic curve

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