Zobrazeno 1 - 10
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pro vyhledávání: '"Selmer IS"'
Autor:
Kling, Anthony, Savoie, Ben
We construct an algorithm to compute the $\varphi$-Selmer group of the elliptic curve $E_b: y^2 = x^3 + b x$ over $\mathbb{Q}(i)$, where $b \in \mathbb{Z}[i]$ and $\varphi$ is a degree 2 isogeny of $E_b$. We associate to $E_b$ a weighted graph $G_b$,
Externí odkaz:
http://arxiv.org/abs/2410.22714
Let $E$ be an elliptic curve with $j$-invariant $0$ or $1728$ and let $\widetilde{E}$ be a $k^{th}$ twist of $E$. We show that for any prime $p$ of good reduction of $\widetilde{E}$, a degree $k$ relative $p$-class group and the root number of $\wide
Externí odkaz:
http://arxiv.org/abs/2412.13022
Let $p$ be an odd prime number and let $K$ be an imaginary quadratic field in which $p$ is split. Let $f$ be a modular form with good reduction at $p$. We study the variation of the Bloch--Kato Selmer groups and the Bloch--Kato--Shafarevich--Tate gro
Externí odkaz:
http://arxiv.org/abs/2409.11966
We prove that the dual fine Selmer group of an abelian variety over the unramified $\mathbb{Z}_{p}$-extension of a function field is finitely generated over $\mathbb{Z}_{p}$. This is a function field version of a conjecture of Coates--Sujatha. We fur
Externí odkaz:
http://arxiv.org/abs/2408.06938
Autor:
Fong, Ho Leung
In this paper, we relate $L(1,\pi,\mathrm{Ad}^\circ)$ to the congruence ideals for cohomological cuspidal automorphic representations $\pi$ of $\mathrm{GL}_n$ over any number field. We then use this result to deduce relationships between the congruen
Externí odkaz:
http://arxiv.org/abs/2409.14933
Autor:
Morgan, Adam
In this note, we provide evidence for a certain twisted version of the parity conjecture for Jacobians, introduced in prior work of V. Dokchitser, Green, Konstantinou and the author. To do this, we use arithmetic duality theorems for abelian varietie
Externí odkaz:
http://arxiv.org/abs/2409.08034
Autor:
Forrás, Ben, Müller, Katharina
Let $E/\mathbb{Q}$ be an elliptic curve and let $p\ge 5$ be a prime of good supersingular reduction. We generalize results due to Meng Fai Lim proving Kida's formula and integrality results for characteristic elements of signed Selmer groups along th
Externí odkaz:
http://arxiv.org/abs/2407.08430
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:
Shingavekar, Pratiksha
Given a sixth power free integer $a$, let $E_a$ be the elliptic curve defined by $y^2=x^3+a$. We prove explicit results for the lower density of sixth power free integers $a$ for which the $3$-isogeny induced Selmer group of $E_a$ over $\mathbb{Q}(\m
Externí odkaz:
http://arxiv.org/abs/2406.03066
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