activity
20072024
most citedOn the Rasmussen-Tamagawa conjecture for QM-abelian surfaces

3 citations · 6 across the 11 of their papers we have counts for

collaborators

11 papers

math.NT2024

-elliptic sheaves and the Hasse principle

Keisuke Arai, Shin Hattori, Satoshi Kondo +1

Let be a rational prime, a power of and . For an integer , let be a central division algebra over of dimension which is spli…

math.NT2023

An equivalent condition for abelian varieties over finite fields to have QM

Keisuke Arai, Yuuki Takai

In this paper, we give an equivalent condition for an abelian variety over a finite field to have multiplication by a quaternion algebra over a number field. We prove the result by…

math.NT2019

Drinfeld-Stuhler modules and the Hasse principle

Keisuke Arai, Satoshi Kondo, Mihran Papikian

We develop a theory of canonical isogeny characters of Drinfeld-Stuhler modules similar to the theory of canonical isogeny characters of abelian surfaces with quaternionic multipli…

math.NT2014

Points on Shimura curves rational over imaginary quadratic fields in the non-split case

Keisuke Arai

For an imaginary quadratic field of class number , we prove that there are only finitely many isomorphism classes of rational indefinite quaternion division algebras su…

math.NT2014★ 1 cited

Non-existence of points rational over number fields on Shimura curves

Keisuke Arai

Jordan, Rotger and de Vera-Piquero proved that Shimura curves have no points rational over imaginary quadratic fields under a certain assumption. In this article, we expand their r…

math.NT2013

Algebraic points on Shimura curves of -type (III)

Keisuke Arai

In previous articles, we classified the characters associated to algebraic points on Shimura curves of -type, and over number fields in a certain large class we showed that…