Zobrazeno 1 - 10
of 42
pro vyhledávání: '"Hashimoto, Sachi"'
Local heights are arithmetic invariants used in the quadratic Chabauty method for determining the rational points on curves. We present an algorithm to compute these local heights for hyperelliptic curves at odd primes $\ell\neq p$. This algorithm si
Externí odkaz:
http://arxiv.org/abs/2401.05228
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:
Hashimoto, Sachi
Let X be an Atkin-Lehner quotient of the modular curve X_0(N) whose Jacobian J_f is a simple quotient of J_0(N)^{new} over Q. We give analytic methods for determining the rational points of X using quadratic Chabauty by explicitly computing two p-adi
Externí odkaz:
https://hdl.handle.net/2144/45282
Self-dual configurations of 2n points in a projective space of dimension n-1 were studied by Coble, Dolgachev-Ortland, and Eisenbud-Popescu. We examine the self-dual matroids and self-dual valuated matroids defined by such configurations, with a focu
Externí odkaz:
http://arxiv.org/abs/2212.05910
Publikováno v:
Expositiones Mathematicae, 41, (2023), no. 3, 631-674
Let $X$ be a curve of genus $g>1$ over $\mathbb{Q}$ whose Jacobian $J$ has Mordell--Weil rank $r$ and N\'eron--Severi rank $\rho$. When $r < g+ \rho - 1$, the geometric quadratic Chabauty method determines a finite set of $p$-adic points containing t
Externí odkaz:
http://arxiv.org/abs/2207.10389
Autor:
Hashimoto, Sachi
Let $X$ be a quotient of the modular curve $X_0(N)$ whose Jacobian $J_X$ is a simple factor of $J_0(N)^{new}$ over $\mathbb{Q}$. Let $f$ be the newform of level $N$ and weight 2 associated with $J_X$; assume $f$ has analytic rank 1. We give analytic
Externí odkaz:
http://arxiv.org/abs/2206.08595
Autor:
Hashimoto, Sachi, Spelier, Pim
The Chabauty-Coleman method is a $p$-adic method for finding all rational points on curves of genus $g$ whose Jacobians have Mordell-Weil rank $r < g$. Recently, Edixhoven and Lido developed a geometric quadratic Chabauty method that was adapted by S
Externí odkaz:
http://arxiv.org/abs/2102.04967
Publikováno v:
Res. number theory 8, 12 (2022)
In this paper we investigate the $\mathbb{Q}$-rational points of a class of simply connected Calabi-Yau threefolds, which were originally studied by Hosono and Takagi in the context of mirror symmetry. These varieties are defined as a linear section
Externí odkaz:
http://arxiv.org/abs/2009.05862
Autor:
Hashimoto, Sachi, Kadets, Borys
A Fano problem is an enumerative problem of counting $r$-dimensional linear subspaces on a complete intersection in $\mathbb{P}^n$ over a field of arbitrary characteristic, whenever the corresponding Fano scheme is finite. A classical example is enum
Externí odkaz:
http://arxiv.org/abs/2002.04580
Autor:
Hashimoto, Sachi, Morrison, Travis
We provably compute the full set of rational points on 1403 Picard curves defined over $\mathbb{Q}$ with Jacobians of Mordell-Weil rank $1$ using the Chabauty-Coleman method. To carry out this computation, we extend Magma code of Balakrishnan and Tui
Externí odkaz:
http://arxiv.org/abs/2002.03291