STUDY OF THE HEIGHTS AND THE DISTRIBUTION OF RATIONAL POINTS ON ALGEBRAIC VARIETIES

代数簇上有理点的高度和分布研究

• 批准号: 10440002
• 负责人: MORITA Yasuo
• 金额: $ 4.35万
• 依托单位: TOHOKU UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 1998
• 资助国家: 日本
• 起止时间: 1998 至 1999
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10440002/
• 关键词: ALGEBRAIC VARIETY; RATIONAL POINTS; HEIGHT; K3 SURFACE; DIOPHANTINE EQUATION; ALGEBRAIC SURFACES; BELIAN VARIETY; 整数点; 数論的幾何学

(A) Morita, Saito, Sato, Siho, and Kajiwara have studied the arithmetic of K3 surface, especially the Galois action on the second etale comomology, and have studied the field of the definition of the corresponding Kuga-Satake abelian variety.(B) Nakamura, Morita, Saito, Siho, Sato, and Kajiwara have studied the arithmetic of abelian varieties.(C) Oda, Ishida, Ogata have studied algebraic varieties which are toric or which are related to automorphic forms, and have studied arithmetic of these varieties.(D) Tanaka have studied Logic and, with Morita, have studied applications of Logic to Number Theory.(E) Hirata and Morita have studied the Baker method, and its application to the estimate of rational points on algebraic curves.

(A)Morita，Saito，Sato，Siho和Kajiwara研究了K_3曲面的算法，特别是第二阶交换簇上的Galois作用，并研究了相应的Kuga-Satake交换簇的定义域。(B)中村、森田、齐藤、四保、佐藤和Kajiwara研究了阿贝尔簇的算术。(C)织田，石田，绪方研究了代数簇是环面或有关自守形式，并研究了这些品种的算术。(D)田中研究了逻辑，并与森田，研究了应用逻辑数论。(E)Hirata和Morita研究了Baker方法，以及它在代数曲线上有理点估计中的应用。

项目成果

Tetsuo Nakamura: "Cyclic torsion of elliptic curves"Proceedings of the American Mathematical Society. 127. 1589-1595 (1999)

Tetsuo Nakamura：“椭圆曲线的循环扭转”美国数学会会刊。

Takeshi Saito: "Weight-monodromy conjecture for l-adic representations associated to modular forms"the proceedings of the CRM summer school"The arithmetic and geometry of algebraic cycles", CRM-AMS, 2000. (印刷中).

Takeshi Saito：“与模形式相关的 l-adic 表示的权重单性猜想”CRM 暑期学校的程序“代数圈的算术和几何”，CRM-AMS，2000 年。（出版中）。

石田正典: "朝倉書店"トーリック多様体入門(印刷中).

Masanori Ishida：《朝仓书店》复曲面流形简介（正在出版）。

Takeshi Saito: "Weight-monodromy conjecture for l-adic representations associated to modular forms"the proceedings of the CRM summer school "The arithmetic and geometry of algebraic cycles",CRM-AMS ,2000. (印刷中).

Takeshi Saito：“与模形式相关的 l-adic 表示的重量单律猜想”CRM 暑期学校的会议记录“代数循环的算术和几何”，CRM-AMS，2000 年。

M.-N.ISHIDA and F.KATO: "The strong rigulity theorem for non-Arclcimedecon uniformigation" Tohoku Mathematical Journal. 50. 537-555 (1998)

M.-N.ISHIDA 和 F.KATO：“非 Arccimedecon 均匀化的强严格性定理”东北数学杂志。