3 citations · 8 across the 13 of their papers we have counts for
14 papers
Exceptional points on Atkin--Lehner quotients
Eran Assaf, Sachi Hashimoto, Ari Shnidman
We study the rational points on the star curve , the quotient of the classical modular curve by the full group of Atkin--Lehner involutions, for s…
Equationless quadratic Chabauty for non-split Cartan modular curves
Sachi Hashimoto, Guido Maria Lido, Davide Lombardo +2
The aim of this article is to describe an equationless method for determining the rational points on the non-split Cartan curve of prime level .…
Hyperelliptic Atkin-Lehner quotients of Shimura curves
Eran Assaf, Sachi Hashimoto
We work towards completely classifying all hyperelliptic Atkin-Lehner quotients of Shimura curves with level coprime to and , extending, on the…
Rational points on modular curves: parameterization and geometric explanations
Maarten Derickx, Sachi Hashimoto, Filip Najman +1
We show that, conditional on Zywina's effective version of the Serre uniformity conjecture, there is a natural way to parameterize non-CM -rational points on all modula…
Local heights on hyperelliptic curves and quadratic Chabauty
L. Alexander Betts, Juanita Duque-Rosero, Sachi Hashimoto +1
Quadratic Chabauty is a -adic method for determining rational points on curves. Local heights are arithmetic invariants used in the quadratic Chabauty method. We present an algo…
Self-dual matroids from canonical curves
Alheydis Geiger, Sachi Hashimoto, Bernd Sturmfels +1
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 s…
Geometric quadratic Chabauty and -adic heights
Juanita Duque-Rosero, Sachi Hashimoto, Pim Spelier
Let be a curve of genus over whose Jacobian has Mordell--Weil rank and Néron--Severi rank . When , the geometric quadratic Chabauty m…
Quadratic Chabauty and -adic Gross-Zagier
Sachi Hashimoto
Let be a quotient of the modular curve whose Jacobian is a simple factor of over . Let be the newform of level and weight 2 as…
A geometric linear Chabauty comparison theorem
Sachi Hashimoto, Pim Spelier
The Chabauty-Coleman method is a -adic method for finding all rational points on curves of genus whose Jacobians have Mordell-Weil rank . Recently, Edixhoven and Lido…
A transcendental Brauer-Manin obstruction to weak approximation on a Calabi-Yau threefold
Sachi Hashimoto, Katrina Honigs, Alicia Lamarche +1
In this paper we investigate the -rational points of a class of simply connected Calabi-Yau threefolds, which were originally studied by Hosono and Takagi in the contex…
38406501359372282063949 & all that: Monodromy of Fano Problems
Sachi Hashimoto, Borys Kadets
A Fano problem is an enumerative problem of counting -dimensional linear subspaces on a complete intersection in over a field of arbitrary characteristic, wheneve…
Chabauty-Coleman computations on rank 1 Picard curves
Sachi Hashimoto, Travis Morrison
We provably compute the full set of rational points on 1403 Picard curves defined over with Jacobians of Mordell-Weil rank using the Chabauty-Coleman method. To ca…
Computing rational points on rank 0 genus 3 hyperelliptic curves
María Inés de Frutos-Fernández, Sachi Hashimoto
We compute rational points on genus odd degree hyperelliptic curves over that have Jacobians of Mordell-Weil rank . The computation applies the Chabauty-Col…
Sharper Lower Bounds in the Maximum Degree and Diameter Bounded Subgraph Problem in the Mesh
Sachi Hashimoto
The Maximum Degree and Diameter Bounded Subgraph Problem (MaxDDBS) asks: given a host graph G, a bound on maximum degree Δ, and a diameter D, what is the largest subgraph of the ho…