ARAI Keisuke

J-GLOBAL         Last updated: Dec 13, 2018 at 03:04
 
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Name
ARAI Keisuke
Affiliation
Tokyo Denki University
Section
School of Science and Technology for Future Life Department of Mathematics
Job title
Associate Professor
Degree
Bachelor(Science)(The University of Tokyo), Master(Mathematical Sciences)(The University of Tokyo), PhD(Mathematical Sciences)(The University of Tokyo)

Research Areas

 
 

Academic & Professional Experience

 
Apr 2005
 - 
Mar 2008
The Univesity of Tokyo Graduate School of Mathematical Sciences Part-time researcher for university or other academic organization
 
Apr 2008
 - 
Mar 2010
Tokyo Denki University School of Engineering, School of Science and Technology for Future Life
 
Sep 2009
 - 
Mar 2010
The University of Tokyo Graduate School of Mathematical Sciences Part-time researcher for university or other academic organization
 
Oct 2009
 - 
Mar 2010
Keio University Faculty of Science and Technology Part-time researcher for university or other academic organization
 

Education

 
Apr 1996
 - 
Mar 2000
Department of Mathematics, Faculty of Science, The University of Tokyo
 
Apr 2000
 - 
Mar 2002
Mathematical Sciences, Graduate School of Mathematical Sciences, The University of Tokyo
 
Apr 2002
 - 
Mar 2005
Mathematical Sciences, Graduate School of Mathematical Sciences, The University of Tokyo
 

Published Papers

 
Contemporary Mathematics   701 9-15   Feb 2018   [Refereed][Invited]
In this note, we survey recent results of the author concerning algebraic points on Shimura curves, especially of Tex-type. These results are based on a joint work of the author and Fumiyuki Momose. We also give several explicit examples.
The Ramanujan Journal   43 15-28   May 2017   [Refereed]
In previous works, we proved that under a certain assumption, the set of rational points over a number field on the Shimura curve of Tex-type consists of at most elliptic points for every sufficiently large prime number Tex. In this arti...
Nagoya Mathematical Journal      Apr 2017   [Refereed]
In a previous article, we proved that Shimura curves have no points rational over number fields under a certain assumption. In this article, we give another criterion of the nonexistence of rational points on Shimura curves and obtain new countere...
Algebraic points on Shimura curves of Tex-type (IV)
RIMS Kokyuroku Bessatsu   B53 3-11   Jun 2016   [Refereed][Invited]
Acta Arithmetica   172(3) 243-250   Feb 2016   [Refereed]
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 results to the case of number fields of higher degree. We also give ...

Misc

 
SGAD2012報告集(仮称)      Apr 2013   [Invited]
楕円曲線のモジュライ空間についてのいくつかの話題の解説
On the lower bound of Galois images associated to elliptic curves
数理解析研究所講究録   1451(代数的整数論とその周辺) 275-284   Oct 2005
代数体上定義された楕円曲線で虚数乗法をもたないものから定まるp進ガロア表現の像は、一様に下に有界であることを示した。さらに、有限個の例外を除いて像の下界を与えた。

Conference Activities & Talks

 
Non-existence of elliptic points on Shimura curves of Tex-type
Jul 2013   
Tex型志村曲線のあるクラスに属する代数体上の点は、素数pが十分大きければ、高々楕円点しかないことを示した。
Non-existence of rational points over number fields on certain Shimura curves
Oct 2013   
Tex型志村曲線のあるクラスに属する代数体上の点は、素数pが十分大きければ、高々楕円点しかないことを示した。
Points on Shimura curves rational over imaginary quadratic fields in the non-split case
日韓整数論セミナー2014   Nov 2014   
虚2次体が四元数環を分解しない場合の志村曲線上の有理点の非存在に関する定理の紹介。ポスター発表。
Points on Shimura curves rational over imaginary quadratic fields in the non-split case
29th Journees Arithmetiques   6 Jul 2015   
For an imaginary quadratic field Tex of class number Tex,
Jordan proved that there are only finitely many isomorphism classes of
rational indefinite quaternion division algebras Tex such that
the associated Shimura curve Tex has Tex-rational po...
Various criterions for non-existence of rational points on Shimura curves [Invited]
2016 Korea-Japan Joint Number theory Seminar   1 Feb 2016   
A Shimura curve can be considered to be an analog of a modular curve.
Non-existence of rational points on Shimura curves has been discussed in several
contexts. In this talk, I will present expansions of known results.

Association Memberships

 
 

Research Grants & Projects

 
Research on rational points on moduli of abelian varieties and related objects
Project Year: Apr 2013 - Mar 2016