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2002 Fiscal Year Final Research Report Summary

Study of relations and applications of Arithmetic Geometry to branches of Algebra

Research Project

Project/Area Number 12440001
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  Tohoku University, Graduate School of Science Professor, 大学院・理学研究科, 教授 (20011653)

Co-Investigator(Kenkyū-buntansha) HIRATA Noriko  Nihon University, Faculty of Science and Technology Professor, 理工学部, 教授 (90215195)
YUKIE Akihiko  Tohoku University, Graduate School of Science Professor, 大学院・理学研究科, 教授 (20312548)
ISHIDA Makoto  Tohoku University, Graduate School of Science Professor, 大学院・理学研究科, 教授 (30124548)
SAITO Takeshi  Tokyo University, Graduate school of Mathematical Science Professor, 大学院・数理科学研究科, 教授 (70201506)
WATANABE Keiichi  Nihon University, Faculty of Literature and Science Professor, 文理学部, 教授 (10087083)
Project Period (FY) 2000 – 2002
KeywordsNumber Theory / Algebraic Geometry / Ring Theory / Group Theory / Representation Theory
Research Abstract

In this research, we have studied relations and applications of Arithmetic Geometry to branches of Algebra. In each year, we have organized an Algebra Symposium which covers all branches of Algebra, a symposium specialized in Ring Theory, and a symposium specialized in Analytic Number Theory. We have organized a symposium specialized in Algebraic Geometry in 2003. We have made a list of research mathematicians working on Algebra also.

  • Research Products

    (14 results)

All Other

All Publications (14 results)

  • [Publications] A.C.Kable, A.Yukie: "The mean value of the product of class numbers of paired quadratic fields I"Tohoku Math.J.. 54. 513-565 (2002)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] A.Yukie: "On the Shintani zeta function for the space of pairs of binary Hermitian forms"J.Number Theory. 54. 205-256 (2002)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] S.David, N.Hirata-Kohno: "Recent progress on linear forms in elliptic logarithms"A Panorama in Number Theory, Cambridge University Press. 26-37 (2002)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] N.Hara, K.Watanabe: "F-regular and F-pure Rings vs. Log-terminal and Log-canonical Singularities"Journal Algebraic Geometry. 11. 363-392 (2002)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Ahmed Abbes, T.Saito: "Ramification of local fields with imperfect residue fields"Americal J.of Mathematics. 124.5. 879-920 (2002)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] G.van der Geer, T.Katura: "An invariant for varieties in positive characteristic"Contemporary Math. 300, in Alg. Number Theory and Alg. Geometry. 131-141 (2002)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 渡辺敬一: "環と体"朝倉書店. 192 (2002)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] A. C. Kable, A. Yukie: "The mean value of the product of class numbers of paired quadratic fields I"Tohoku Math. J.. 54. 513-565 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] A. Yukie: "On the Shintani zeta function for the space of pairs of binary Hermitian forms"J. Number Theory. 54. 205-256 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] S. David, N. Hirata-Kohno: "Recent progress on linear forms in elliptic logarithms"A Panorama in Number Theory. 26-37 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] N. Hara, K. Watanabe: "F-regular and F-pure Rings vs. Log-terminal and Log-canonical Singularities"Journal Algebraic Geometry. 11. 363-392 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Ahmed Abbes, T. Saito: "Ramification of local fields with imperfect residue fields"Americal J. of Mathematics. 124.5. 879-920 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] G. van der Geer, T. Katura: "An invariant for varieties in positive characteristic"Contemporary Math. 300, in Alg. Number Theory and Alg. Geometry. 131-141 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Keiichi Watanabe: "Rings and Fields"Asakura Shoten. 1-192 (2002)

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

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Published: 2004-04-14  

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