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1999 Fiscal Year Final Research Report Summary

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

Research Project

Project/Area Number 10440002
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionTOHOKU UNIVERSITY

Principal Investigator

MORITA Yasuo  THE GRADUATE SCHOOL OF SCIENCE, Tohoku University, PROFESSOR, 大学院・理学研究科, 教授 (20011653)

Co-Investigator(Kenkyū-buntansha) TANAKA Kazuyuki  THE GRADUATE SCHOOL OF SCIENCE, Tohoku University, PROFESSOR, 大学院・理学研究科, 教授 (70188291)
NAKAMURA Tetsuo  THE GRADUATE SCHOOL OF SCIENCE, Tohoku University, PROFESSOR, 大学院・理学研究科, 教授 (90016147)
ODA Tadao  THE GRADUATE SCHOOL OF SCIENCE, Tohoku University, PROFESSOR, 大学院・理学研究科, 教授 (60022555)
SAITO Takeshi  THE GRADUATE SCHOOL OF MATHEMATICAL SCIENCE, TOKYO UNIVERSITY, ASSOCIATE PROFESSOR, 大学院・数理科学研究科, 助教授 (70201506)
OGATA Syoetsu  THE GRADUATE SCHOOL OF SCIENCE, Tohoku University, ASSOCIATE PROFESOR, 大学院・理学研究科, 助教授 (90177113)
Project Period (FY) 1998 – 1999
KeywordsALGEBRAIC VARIETY / RATIONAL POINTS / HEIGHT / K3 SURFACE / DIOPHANTINE EQUATION / ALGEBRAIC SURFACES / BELIAN VARIETY
Research Abstract

(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.

  • Research Products

    (16 results)

All Other

All Publications (16 results)

  • [Publications] Yasuo Morita: "Tate's conjectures for the second etale cohomologies of abelian surfaces"Advanced Studies in Contemporary Mathematics. 1. 45-56 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Tetsuo Nakamura: "Cyclic torsion of elliptic curves"Proceedings of the American Mathematical Society. 127. 1589-1595 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Tetsuo Nakamura: "Q-curves with complex multiplication"Proceedings of the American Mathematical Society. (印刷中).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] K.Tanaka and T.Yamazaki: "A non-standard construction of Haar measure and WKL_0"Journal of Symbolic Logic. (印刷中).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 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).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Takeshi Saito and Qing Liu: "Inequality for conductor and differentials of a curve over a local field"Journal of Algebraic Geometry. (印刷中).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 森田康夫: "東京大学出版会"整数論. 284 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 石田正典: "朝倉書店"トーリック多様体入門(印刷中).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] YASUO MORITA: "TATE'S CONJECTURES FOR THE SECOND ETALE COHOMOLOGIES OF ABELIAN VARIETIES"ADVANCED STUDIES IN CONTEMPORARY MATHEMATICS. 1. 45-56 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] TETSUO NAKAMURA: "CYCLIC TORSION OF ELLIPTIC CURVES"PROCEEDINGS OF AMERICAN MATHEMATICAL SOCIETY. 127. 1589-1595 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] TETSUO NAKAMURA: "Q-CURVES WITH COMPLEX MULTIPLICATION"PROCEEDINGS OF AMERICAL MATHEMATICAL SOCIETY. (IN PRESS).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] KAZUYUKI TANAKA AND TADASHI YAMAZAKI: "A NON-STANDARD CONSTRUCTION OF HARR MEASURE AND WLKLィイD2OィエD2"JOURNAL OF SYMBOLIC LOGIC. (IN PRESS).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] TAKESHI SAITO: "WEIGHT-MONODOROMY CONJECTURE FOR l-ADIC REPRESENTATIONS ASSOCIATED TO MODULAR FORMS"THE PROCEEDINGS OF THE CRM SUMMER SCHOOL. (IN PRESS).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] TAKESHI SAITO: "INEQUALITY FOR CONDUCTOR AND DIFFERENTIALS OF A CURVE OVER A LOCAL FIELD"JOURNAL OF ALGEBRA. (IN PRESS).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] YASUO MORITA: "NUMBER THEORY (IN JAPANESE)"TOKYO UNIVERSITY PRESS. 284 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] ISHIDA MAKOTO: "INTRODUCTION TO TORIC VARIETIES (IN JAPANESE)"ASAKURA SHOTEN (IN PRESS).

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 2001-10-23  

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