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pro vyhledávání: '"Daniels, Harris B."'
Let $E/\mathbb{Q}$ be an elliptic curve, let $\overline{\mathbb{Q}}$ be a fixed algebraic closure of $\mathbb{Q}$, and let $G_{\mathbb{Q}}=\text{Gal}(\overline{\mathbb{Q}}/\mathbb{Q})$ be the absolute Galois group of $\mathbb{Q}$. The action of $G_{\
Externí odkaz:
http://arxiv.org/abs/2105.02060
Autor:
Daniels, Harris B.
In [2], the author claims that the fields $\mathbb{Q}(D_4^\infty)$ defined in the paper and the compositum of all $D_4$ extensions of $\mathbb{Q}$ coincide. The proof of this claim depends on a misreading of a celebrated result by Shafarevich. The pu
Externí odkaz:
http://arxiv.org/abs/2102.12653
Autor:
Daniels, Harris B., Morrow, Jackson S.
In this paper, we initiate a systematic study of entanglements of division fields from a group theoretic perspective. For a positive integer $n$ and a subgroup $G\subseteq \text{GL}_2(\mathbb{Z}/{n}\mathbb{Z})$ with surjective determinant, we provide
Externí odkaz:
http://arxiv.org/abs/2008.09886
Let $E$ be an elliptic curve defined over $\mathbb{Q}$, and let $\rho_E\colon {\rm Gal}(\overline{\mathbb{Q}}/\mathbb{Q})\to {\rm GL}(2,\widehat{ \mathbb{Z} })$ be the adelic representation associated to the natural action of Galois on the torsion po
Externí odkaz:
http://arxiv.org/abs/1912.05618
Publikováno v:
Exp. Math. 31 (2022), no. 2, 518-536
Let $E$ be an elliptic curve without complex multiplication defined over the rationals. The purpose of this article is to define a positive integer $A(E)$, that we call the {\it Serre's constant associated to $E$}, that gives necessary conditions to
Externí odkaz:
http://arxiv.org/abs/1812.04133
We determine, for an elliptic curve $E/\mathbb Q$ and for all $p$, all the possible torsion groups $E(\mathbb Q_{\infty, p})_{tors}$, where $\mathbb Q_{\infty, p}$ is the $\mathbb Z_p$-extension of $\mathbb Q$.
Comment: 20 pages
Comment: 20 pages
Externí odkaz:
http://arxiv.org/abs/1808.05243
Publikováno v:
Math. Comp. 89 (2020) 411-439
Given an elliptic curve $E/\mathbb{Q}$ with torsion subgroup $G = E(\mathbb{Q})_{\rm tors}$ we study what groups (up to isomorphism) can occur as the torsion subgroup of $E$ base-extended to $K$, a degree 6 extension of $\mathbb{Q}$. We also determin
Externí odkaz:
http://arxiv.org/abs/1808.02887
Publikováno v:
Transactions of the London Mathematical Society, Vol. 6, No. 1 (2019), 22-52
Recently there has been much interest in studying the torsion subgroups of elliptic curves base-extended to infinite extensions of $\mathbb{Q}$. In this paper, given a finite group $G$, we study what happens with the torsion of an elliptic curve $E$
Externí odkaz:
http://arxiv.org/abs/1803.09614
Autor:
Daniels, Harris B.
Let $E/\mathbb{Q}$ be an elliptic curve and let $\mathbb{Q}(D_4^\infty)$ be the compositum of all extensions of $\mathbb{Q}$ whose Galois closure has Galois group isomorphic to a quotient of a subdirect product of a finite number of transitive subgro
Externí odkaz:
http://arxiv.org/abs/1710.05228
In this article we extend work of Shanks and Washington on cyclic extensions, and elliptic curves associated to the simplest cubic fields. In particular, we give families of examples of hyperelliptic curves $C: y^2=f(x)$ defined over $\mathbb{Q}$, wi
Externí odkaz:
http://arxiv.org/abs/1708.07896