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Arithmetic of algebraic groups and their homogeneous spaces

Research Project

Project/Area Number 11640017
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research Institutionkanazawa University

Principal Investigator

MORISHITA Masanon  Kanazawa Univ. Fac. Science Assoc.Prof., 理学部, 助教授 (40242515)

Co-Investigator(Kenkyū-buntansha) TOMARI Masataka  Kanazawa Univ. Fac. Science Assoc.Prof., 理学部, 助教授 (60183878)
SUGANO Takashi  Kanazawa Univ. Fac. Science Prof., 理学部, 教授 (30183841)
WATANABE Takao  Osaka Univ. Grad. School Assoc.Prof., 大学院・理学研究科, 助教授 (30201198)
HAYAICAWA Takayuki  Kanazawa Univ. Fac. Science Assistant, 理学部, 助手 (20198823)
伊藤 達郎  金沢大学, 理学部, 教授 (90015909)
Project Period (FY) 1999 – 2000
Project Status Completed (Fiscal Year 2000)
Budget Amount *help
¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 2000: ¥1,700,000 (Direct Cost: ¥1,700,000)
Fiscal Year 1999: ¥1,800,000 (Direct Cost: ¥1,800,000)
KeywordsPrime / Knot / number field / 3-manifold / 代数群 / ガロアコホモロジー / ガロア群 / 絡み目群 / ミルナー不変量 / レダイ記号
Research Abstract

M.Morishita initiated to study analogies between primes and knots, 3-manifolds and number fields. Based on and analogy. Between the structures of Galois and link groups. He published a paper and submitted a paper on this research, and he gave talks at some symposiums in Japan and U.S.A.M.Morishita gave a summary talk on the geometry and Riemunn-Roch theorem at a workshop on Index Theorem in Japan. M.Morishita worked jointly with Prof. Murasugi at Toronto Univ. On a theory of genera for links and obtained some results, and he it preparing a paper on this topic.

Report

(3 results)
  • 2000 Annual Research Report   Final Research Report Summary
  • 1999 Annual Research Report
  • Research Products

    (8 results)

All Other

All Publications (8 results)

  • [Publications] M.Morishita,T.Watanabe: "Adele geometry of numbers."The Advanced Studies in Pure Math.serres.. 30. (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] M.Morishita: "Milnor's link invariants attached to certain Galois groups over Q."Proceeding Japan Academy. 76. 18-21 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] M.Morishita and T.Watanabe: "Adele geometry of numbers."The Advanced Studies in Pure Mathematics. vol.30. (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] M.Morishita: "Milnor's link invariants affached to certain Galois groups aven.Q"Proe.Japan Academg. vol.76. 18-21 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] M.Morishita,T.Watarobe: "Adele geometry of numbers."The Advanced Studies in pure Math.Series. (to appear).

    • Related Report
      2000 Annual Research Report
  • [Publications] M.Morishita: "Milnor's link invariants attached to certain Galois groups over Q"Proc.Japan Academy. 76. 18-21 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] M. Morishita and T. Watanabe: "Adele Geometry of Numbers"Advanced Studies in Pure Mathematics. (To appear).

    • Related Report
      1999 Annual Research Report
  • [Publications] M. Morishita: "Milnor's link invariants attached to certain Galois groups over Q"Proceeding of Japan Academy. vol76,No2. (未確定) (2000)

    • Related Report
      1999 Annual Research Report

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Published: 1999-04-01   Modified: 2016-04-21  

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