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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)
伊吹山 知義  大阪大学, 大学院・理学研究科, 教授 (60011722)
向井 茂  名古屋大学, 大学院・多元数理研究科, 教授 (80115641)
坂内 英一  九州大学, 大学院・数理学研究科, 教授 (10011652)
Project Period (FY) 2000 – 2002
Project Status Completed (Fiscal Year 2002)
Budget Amount *help
¥15,200,000 (Direct Cost: ¥15,200,000)
Fiscal Year 2002: ¥4,700,000 (Direct Cost: ¥4,700,000)
Fiscal Year 2001: ¥4,700,000 (Direct Cost: ¥4,700,000)
Fiscal Year 2000: ¥5,800,000 (Direct Cost: ¥5,800,000)
KeywordsNumber Theory / Algebraic Geometry / Ring Theory / Group Theory / Representation Theory / 数論的幾何学 / 代数学 / 整数論 / 代数幾何学 / 解析数論
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.

Report

(4 results)
  • 2002 Annual Research Report   Final Research Report Summary
  • 2001 Annual Research Report
  • 2000 Annual Research Report
  • Research Products

    (36 results)

All Other

All Publications (36 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
    • Related Report
      2002 Final Research Report Summary
  • [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
    • Related Report
      2002 Final Research Report Summary
  • [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
    • Related Report
      2002 Final Research Report Summary
  • [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
    • Related Report
      2002 Final Research Report Summary
  • [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
    • Related Report
      2002 Final Research Report Summary
  • [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
    • Related Report
      2002 Final Research Report Summary
  • [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
    • Related Report
      2002 Final Research Report Summary
  • [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
    • Related Report
      2002 Final Research Report Summary
  • [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
    • Related Report
      2002 Final Research Report Summary
  • [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
    • Related Report
      2002 Final Research Report Summary
  • [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
    • Related Report
      2002 Final Research Report Summary
  • [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
    • Related Report
      2002 Final Research Report Summary
  • [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
    • Related Report
      2002 Final Research Report Summary
  • [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
    • Related Report
      2002 Final Research Report Summary
  • [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)

    • Related Report
      2002 Annual Research Report
  • [Publications] A.Yukie: "On the Shintani zeta function for the space of pairs of binary Hermitian forms"J. Number Theory. 54. 205-256 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] S.David, N.Hirata-Kohno: "Recent prpgress on linear foms in elliptic logarithms"A Panorama in Number Theory, Cambridge University Press. 26-37 (2002)

    • Related Report
      2002 Annual Research Report
  • [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)

    • Related Report
      2002 Annual Research Report
  • [Publications] Ahmed Abbes, T.Saito: "Ramification of local fields with imperfect residue fields"Americal J. of Mathematics. 124.5. 879-920 (2002)

    • Related Report
      2002 Annual Research Report
  • [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)

    • Related Report
      2002 Annual Research Report
  • [Publications] 渡辺敬一: "朝倉書店"環と体. 192 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Akihiko Yukie: "On the Shintani zeta function for the space of pairs of binary Hermitian forms"J. Number Theory. (To appear).

    • Related Report
      2001 Annual Research Report
  • [Publications] Tomoyoshi Ibukiyama, Hidenori Katsurada: "On squared Mobius function for half integral matrices and its application"J. Number Theory. (To appear).

    • Related Report
      2001 Annual Research Report
  • [Publications] E.Bannai, M.Koike, A.Munemasa, d J.Sekiguti: "Some Results on Modular Forms -Subgroups of the Modular Group Whose Ring of Modular Forms is a Polynomial Ring"Advanced Studies in Pure Math. 32. 245-254 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] S.DAVID nad N.HIRATA-KOHNO: "Recent progress on linear forms in elliptic logarithms"the Proc. of the Conference "A Panorama in Number Theory", Cambridge University Press. (To appear).

    • Related Report
      2001 Annual Research Report
  • [Publications] K.Watanabe, S.Goto, S.Iai: "Good ideals in Gorenstein local rings"Trans. A. M. S.. 353. 2309-2346 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] H.Yoshida: "Motives and Siegel modular forms"American Journal of Mathematics. 123. 1171-1197 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] 荒川恒男, 伊吹山知義他: "ベルヌーイ数とゼータ関数"牧野書店. 243 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] 森田康夫: "コンピューターの安全を守る素数"AERAMook. 61. 54-57 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] E.Bannai and M.Koike: "Some results on modular forms-subgroups of the modular group whose ring of modular forms is a polynomial ring"to appear in Advanced Studies in Pure Mathematics. (2001)

    • Related Report
      2000 Annual Research Report
  • [Publications] T.Saito and Q.Liu: "Inequality for conductor and differentials of a curve over a local field"Journal of Algebraic Geometry. 9. 409-424 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Tomoyoshi Ibukiyama: "Modular forms of rational weights and modular varieties"Abhand.Math.Semi.Univ.Hamburg. 70. 315-339 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] K.Watanabe and K.Yoshida: "Hilbert-Kunz multiplicity and an inequality between multiplicity and colength"Journal of Algebra. 230. 295-317 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] N.Hirata-Kohno and S.David: "Recent progress on linear forms in elliptic logarithms"to appear in the Proceedings of the Conference "Number Theory at the Gateway of Millennium". (2001)

    • Related Report
      2000 Annual Research Report
  • [Publications] 向井茂(青木和彦等 編): "モジュライ理論II"岩波書店. 291 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] 斎藤毅: "数論1(現代数学の基礎10)"岩波書店. 172 (2000)

    • Related Report
      2000 Annual Research Report

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Published: 2000-04-01   Modified: 2016-04-21  

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