Zobrazeno 1 - 10
of 1 118
pro vyhledávání: '"14H52"'
Autor:
Banerjee, Kuntal, Rayan, Steven
We explore very stable and wobbly bundles, twisted in a particular sense by a line bundle, over complex algebraic curves of genus $1$. We verify that twisted stable bundles on an elliptic curve are not very stable for any positive twist. We utilize s
Externí odkaz:
http://arxiv.org/abs/2411.06335
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
In this paper, we define a version of the arithmetic-geometric mean (AGM) function for arbitrary finite fields $\mathbb{F}_q$, and study the resulting AGM graph with points $(a,b) \in \mathbb{F}_q \times \mathbb{F}_q$ and directed edges between point
Externí odkaz:
http://arxiv.org/abs/2410.17969
Autor:
Choi, Seokhyun, Im, Bo-Hae
We prove that if $f:X \rightarrow A$ is a morphism from a smooth projective variety $X$ to an abelian variety $A$ over a number field $K$, $G$ is a subgroup of automorphisms of $X$ satisfying certain properties, and if a prime $p$ divides the order o
Externí odkaz:
http://arxiv.org/abs/2410.16867
Brandt--Sohn correspondence shows a connection between maximal orders in quaternion algebra $B_{p,\infty}$ and ternary quadratic forms with discriminant $p$. In this paper, we use this correspondence to compute endomorphism rings of supersingular ell
Externí odkaz:
http://arxiv.org/abs/2409.11025
Autor:
Daniels, Harris, Rouse, Jeremy
Let $E/\mathbb{Q}$ be an elliptic curve. We say that $E$ has a near coincidence of level $(n,m)$ if $m \mid n$ and $\mathbb{Q}(E[n]) = \mathbb{Q}(E[m],\zeta_{n})$. In the present paper we classify near coincidences of prime power level. We use this r
Externí odkaz:
http://arxiv.org/abs/2409.00881
Let $S_l(M,N)$ denote a set of $\ell$ triples of positive integers whose parts have the same sum $M$ and the same product $N$. For each $2\leq\ell\leq 4$ we establish a connection between the set $S_l(M,N)$ and a family of elliptic curves. When $\ell
Externí odkaz:
http://arxiv.org/abs/2408.13867
Autor:
Laishram, Shanta, Sahoo, Satyabrat
Let $K$ be a number field, and $\mathcal{O}_K$ be the ring of integers of $K$. In this article, we study the solutions of the generalized Fruit Diophantine equation $ax^d-y^2-z^2 +xyz-b=0$ over $K$, where $a\in \mathcal{O}_K\setminus \{0\}$, $b \in \
Externí odkaz:
http://arxiv.org/abs/2408.12278
For each prime number $\ell$ and for each imaginary quadratic order of class number one or two, we determine all the possible $\ell$-adic Galois representations that occur for any elliptic curve with complex multiplication by such an order over its m
Externí odkaz:
http://arxiv.org/abs/2408.04159
We prove that the Hessian transformation of a plane projective cubic corresponds to a $3$-endomorphism of a model elliptic curve. By exploiting this result, we investigate a family of functional graphs -- called Hessian graphs -- defined by the Hessi
Externí odkaz:
http://arxiv.org/abs/2407.17042