Zobrazeno 1 - 10
of 48
pro vyhledávání: '"Keller, Timo"'
Autor:
Keller, Timo, Stoll, Michael
Publikováno v:
Comptes Rendus. Mathématique, Vol 360, Iss G5, Pp 483-489 (2022)
Let $X$ be one of the $28$ Atkin–Lehner quotients of a curve $X_0(N)$ such that $X$ has genus $2$ and its Jacobian variety $J$ is absolutely simple. We show that the Shafarevich–Tate group $\Sha (J/\mathbb{Q})$ is trivial. This verifies the stron
Externí odkaz:
https://doaj.org/article/a74adc68d6ea4ace994328262224ff64
Autor:
Keller, Timo, Yin, Mulun
Let $f$ be a newform of weight $k$ and level $N$ with trivial nebentypus. Let $\mathfrak{p}\nmid 2N$ be a maximal prime ideal of the coefficient ring of $f$ such that the self-dual twist of the mod-$\mathfrak{p}$ Galois representation of $f$ is reduc
Externí odkaz:
http://arxiv.org/abs/2402.12781
Autor:
Keller, Timo, Stoll, Michael
We develop the theory and algorithms necessary to be able to verify the strong Birch--Swinnerton-Dyer Conjecture for absolutely simple modular abelian varieties over $\mathbf{Q}$. We apply our methods to all 28 Atkin--Lehner quotients of $X_0(N)$ of
Externí odkaz:
http://arxiv.org/abs/2312.07307
Autor:
Bourdon, Abbey, Hashimoto, Sachi, Keller, Timo, Klagsbrun, Zev, Lowry-Duda, David, Morrison, Travis, Najman, Filip, Shukla, Himanshu
We develop an algorithm to test whether a non-CM elliptic curve $E/\mathbb{Q}$ gives rise to an isolated point of any degree on any modular curve of the form $X_1(N)$. This builds on prior work of Zywina which gives a method for computing the image o
Externí odkaz:
http://arxiv.org/abs/2311.07740
Autor:
Adžaga, Nikola, Keller, Timo, Michaud-Jacobs, Philippe, Najman, Filip, Ozman, Ekin, Vukorepa, Borna
In this paper we improve on existing methods to compute quadratic points on modular curves and apply them to successfully find all the quadratic points on all modular curves $X_0(N)$ of genus up to $8$, and genus up to $10$ with $N$ prime, for which
Externí odkaz:
http://arxiv.org/abs/2303.12566
Autor:
Keller, Timo
Using the Shioda-Tate theorem and an adaptation of Silverman's specialization theorem, we reduce the specialization of Mordell-Weil ranks for abelian varieties over fields finitely generated over infinite finitely generated fields $k$ to the the spec
Externí odkaz:
http://arxiv.org/abs/2301.12816
Autor:
Keller, Timo
We prove a finiteness theorem for the first flat cohomology group of finite flat group schemes over integral normal proper varieties over finite fields. As a consequence, we can prove the invariance of the finiteness of the Tate-Shafarevich group of
Externí odkaz:
http://arxiv.org/abs/2203.05798
We complete the computation of all $\mathbb{Q}$-rational points on all the $64$ maximal Atkin-Lehner quotients $X_0(N)^*$ such that the quotient is hyperelliptic. To achieve this, we use a combination of various methods, namely the classical Chabauty
Externí odkaz:
http://arxiv.org/abs/2203.05541
Autor:
Keller, Timo, Stoll, Michael
Let $X$ be one of the $28$ Atkin-Lehner quotients of a curve $X_0(N)$ such that $X$ has genus $2$ and its Jacobian variety $J$ is absolutely simple. We show that the Shafarevich-Tate group of $J/\mathbb{Q}$ is trivial. This verifies the strong BSD co
Externí odkaz:
http://arxiv.org/abs/2107.00325
Autor:
Adžaga, Nikola, Arul, Vishal, Beneish, Lea, Chen, Mingjie, Chidambaram, Shiva, Keller, Timo, Wen, Boya
We use the method of quadratic Chabauty on the quotients $X_0^+(N)$ of modular curves $X_0(N)$ by their Fricke involutions to provably compute all the rational points of these curves for prime levels $N$ of genus four, five, and six. We find that the
Externí odkaz:
http://arxiv.org/abs/2105.04811