Zobrazeno 1 - 10
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pro vyhledávání: '"Selmer group"'
Autor:
Ghosh, Sohan, Ray, Jishnu
Consider a function field $K$ with characteristic $p>0$. We investigate the $\Lambda$-module structure of the Mordell-Weil group of an abelian variety over $\mathbb{Z}_p$-extensions of $K$, generalizing results due to Lee. Next, we study the algebrai
Externí odkaz:
http://arxiv.org/abs/2406.03201
Autor:
Koymans, Peter, Smith, Alexander
Recently, Alp\"oge-Bhargava-Shnidman determined the average size of the $2$-Selmer group in the cubic twist family of any elliptic curve over $\mathbb{Q}$ with $j$-invariant $0$. We obtain the distribution of the $3$-Selmer groups in the same family.
Externí odkaz:
http://arxiv.org/abs/2405.09311
Akademický článek
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Let $\mathcal{C}$ be a hyperelliptic curve $y^2 = p(x)$ defined over a number field $K$ with $p(x)$ integral of odd degree. The purpose of the present article is to prove lower and upper bounds for the $2$-Selmer group of the Jacobian of $\mathcal{C}
Externí odkaz:
http://arxiv.org/abs/2308.08663
Autor:
YAN, Jiali
Publikováno v:
Journal de Théorie des Nombres de Bordeaux, 2023 Jan 01. 35(3), 659-674.
Externí odkaz:
https://www.jstor.org/stable/48766115
Autor:
Shii, Ryota
Let $K$ be an imaginary quadratic field where $p$ is inert. Let $E$ be an elliptic curve defined over $K$ and suppose that $E$ has good supersingular reduction at $p$. In this paper, we prove that the plus/minus Selmer group of $E$ over the anticyclo
Externí odkaz:
http://arxiv.org/abs/2308.16384
A generalization of the congruent number problem is to find positive integers $n$ that appear as the areas of Heron triangles. Selmer group of a congruent number elliptic curve has been studied quite extensively. Here, we look into the $2$-Selmer gro
Externí odkaz:
http://arxiv.org/abs/2301.08099
Autor:
Ray, Anwesh
Let $p$ be an odd prime and $F_\infty$ be a $\mathbb{Z}_p$-extension of a number field $F$. Given an elliptic curve $E$ over $F$, we study the structure of the fine Selmer group over $F_\infty$. It is shown that under certain conditions, the fine Sel
Externí odkaz:
http://arxiv.org/abs/2208.13247
Given an elliptic curve $E$ over a number field $F$ and an isogeny $\varphi$ of $E$ defined over $F$, the study of the $\varphi$-Selmer group has a rich history going back to the works of Cassels and the recent works of Bhargava et al. and Chao Li. L
Externí odkaz:
http://arxiv.org/abs/2207.12487
Akademický článek
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