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SYNTHETIC RESEARCHES IN ALGEBRA AND ITS RELATED FIELDS

Research Project

Project/Area Number 60302002
Research Category

Grant-in-Aid for Co-operative Research (A)

Allocation TypeSingle-year Grants
Research Field 代数学・幾何学
Research InstitutionKyushu University

Principal Investigator

SHIRATANI KATSUMI  KYUSHU UNIVERSITY,FACULTY OF SCIENCE,PROFESSOR, 理学部, 教授 (80037168)

Co-Investigator(Kenkyū-buntansha) ODA TADAO  TOHOKU UNIVERSITY,FACULTY OF SCIENCE,PROFESSOR, 理学部, 教授 (60022555)
IHARA YASUTAKA  UNIVERSITY OF TOKYO,FACULTY OF SCIENCE,PROFESSOR, 理学部, 教授 (70011484)
TACHIKAWA HIROYUKI  TSUKUBA UNIVERSITY,INSTITUTE OF MATHEMATICS,PROFESSOR, 数学系, 教授 (20015473)
IWAHORI NAGAYOSHI  JOCHI UNIVERSITY,FACULTY OF SCIENCE AND TECHNOLOGY,PROFESSOR, 理工学部, 教授 (60011417)
NAGATA MASAYOSHI  KYOTO UNIVERSITY,FACULTY OF SCIENCE, PROFESSOR, 理学部, 教授 (00025230)
Project Period (FY) 1985 – 1987
Project Status Completed (Fiscal Year 1987)
Budget Amount *help
¥27,200,000 (Direct Cost: ¥27,200,000)
Fiscal Year 1987: ¥8,000,000 (Direct Cost: ¥8,000,000)
Fiscal Year 1986: ¥8,000,000 (Direct Cost: ¥8,000,000)
Fiscal Year 1985: ¥11,200,000 (Direct Cost: ¥11,200,000)
KeywordsRamification Theory of Surfaces / Braid Group / Uniruled Variety / Reciprocity Laws Hadamard Matrix / Simple Group / Galois Representation / ガロア表現 / デインキン数学 / uniruled variety / Buchsbaum環 / 群環 / 保型形式 / ホップ代数
Research Abstract

IN THIS RESEARCH PROJECT THE 31TH, 32TH, 33TH SYMPOSIUMS OF ALGEBRA AND THE SEVERAL INDIVIDUAL SYMPOSIUMS WERE HELD, SO THAT THEY OFFERED VARIOUS RESEARCH DIRECTIONS, SUGGESTIONS TO ALL CORESEARCHERS WORKING IN THE ALGEBRA FIRELD OF JAPAN.
SOLUTION OF SERRE'S CONJECTURE IN 2-DIMENSIONAL CASE BY CONSTRUCTING A RAMIFICATION THEORY FOR SURFACES WITH SYSTEMATIC USE OF NUMVER THEORETIC METHOD IN ALGEBRAIC GEOMETRY, CONSTRUCTION OF THE THEORY OF RAMIFIED GALOIS COVERINGS BY MAKING USE OF BRAID GROUPS AND ITS APPLICATION TO GALOIS REPRESENTATION AND JACOBI SUMS, INTRODUCTION OF A NEW CONCEPT OF HIGHER CIRCULAR UNIT, AND AN ORGANIC INTERPRETATION OF EXPLICIT RECIPROCITY LAWS THROUGH CRYSTALLINE COHOMOLOGY WITH POSSIBILITY OF ITS GENERALIZATION TO MORE GENERAL COMMUTATIVE RINGS.
AS FOR THE GROUP THEORY, HALL'S CONJECTURE, JANUSZ'S CONJECTURE WERE SOLVED AS AN APPLICATION OF THE CLASSIFICATION THEOREM OF FINITE SIMPLE GROUPS. IN THE COMBINATORIAL THEORY IT IS NOTICEABLE THAT A NUMBER THEORETIC CON … More STRUCTION OF SOME HADAMARD MATRICES AND SEVERAL NEW POLYNOMIAL INVARIANTS ON IWAHORI ALGEBRA AND LINKS WERE GIVEN. IT IS ALSO WORTHWHILE THAT IN ALGEBRAIC GEOMETRY A STRUCTURE THEORY OF UNIRULED VARIETIES OVER ALGEBRAICALLY CLOSED FIELDS WAS SHOWN, THE CONCEPT OF FINITE REPRESENTATION TYPE IN ALGEBRA THEORY WAS INTRODUCED TO COMMUTATIVE RINGS, AND AN EXPLICIT STUDY ON BUCHSBAUM RING WAS DEVELOPPED TO LARGE EXTENT.
FINALLY, IN THE SYMPOSIUMS ON DYNKIN MATHEMATICS, GEOMETRY AND AUTOMORPHIC FORMS IT WAS AIMED TO INTERCHANGE THEIR RESEARCHES AMONG SOME GEOMETERS, PHYSICISTS AND ALGEBRAISTS, SO THAT VARIOUS IMPORTANT RESULTS WERE OBTAINED ON DYNKIN DIAGRAMS FROM STATISTICAL PHYSICS, SINGULARLITIES, GEOMETRIES AND NUMBER THEORY OF SYMMETRIC SPACES.
AS IN THE ABOVE, CERTAIN SYNTHETIC, ORGANIC DEVELOPMENTS WERE MADE ON IMPORTANT SUBJECTS NOWADAYS IN THE AREA OF ALGEBRA AND ITS RELATED FIELDS, THERETHROUGH ALL RESEARCHERS IN RELATED FIELDS WERE AFFECTED GOOD INFLUENCES, ENCOURAGEMENTS. CONSEQUENTLY, A GREAT PROGRESS IN THE ALGEBRA FIELD OF JAPAN WAS MADE WIDELY AND REMARKABLY. Less

Report

(2 results)
  • 1987 Final Research Report Summary
  • 1986 Annual Research Report

Research Products

(48 results)

All Other

All Publications (48 results)

  • [Publications] 北詰正顕 外 白谷克巳 編: 第31回代数学シンポジウム報告集. 1-321 (1985)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] 斎藤秀司 外 白谷克巳 編: 第32回代数学シンポジウム報告集. 1-327 (1986)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] 片山真一 外 白谷克巳 編: 第33回代数学シンポジウム報告集. 1-338 (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] KADO,J. 外 大城紀代市 編: PROCEEDINGS OF THE 18TH SYMPOSIUM ON RING THEORY. 1-115 (1985)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] HIRATA, K. 外 岩永恭雄 編: PROCEEDINGS OF THE 19TH SYMPOSIUM ON RING THEORY. 1-106 (1986)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] MARUBAYASHI;H・UEDA,A 外 丸林英俊 編: PROCEEDINGS OF THE 20TH SYMPOSIUM ON RING THEORY. 1-145 (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] 谷崎俊之 外 阿部英一 編: 「代数群,リー環とその表現・ホップ代数とガロア理論」シンポジウム報告集. 1-268 (1986)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] 山形邦夫 外 太刀川弘幸 編: 多元環の表現論シンポジウム報告集. 1-235 (1986)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] SHOJI, K 外: Proceedings of The 10th Symposium on Semigroups. 1-83 (1986)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] 小関道夫 外 白谷克巳 編: 整数論研究会記録. 1-37 (1986)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] 伊藤昇 外 大山豪 編: 代数的組合せ論報告集. 1-168 (1986)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] 三木博雄 外 森田康夫 編: 数論研究集会報告集. 1-158 (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] 若松隆義 外 山形邦夫 編: 多元環の表現論シンポジウム報告集. 1-176 (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] 吉田知行 外 竹内光弘 編: Dynkin 数学研究集会報告集. 1-207 (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] ODA, Tadao: "Convex Bodies and Algebraic Geometry" Springer-Verlag, 280 (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] KITAOKA, Yoshiyuki: "Lectures on Siegel Modular Forms and Representation by Quadratic Forms" Springer-Verlag, 227 (1986)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] KITAZUME, M. AND 20 OTHERS: "CONWAY-NORTON ALGEBRAS AND THEIR AUTOMORPHISM GROUP, AND 15 OTHER ARTICLES" REPORTS OF THE 31TH SYMPOSIUM OF ALGEBRA (EDITED BY K. SHIRATANI). KANAZAWA UNIV.1-321 (1985)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] SAITO, S. AND 20 OTHERS: "INTERSECTION THEORY ON ARITHMETIC SURFACES, AND 19 OTHER ARTICLES" REPORTS OF THE 32TH SYMPOSIUM OF ALGEBRA (EDITED BY K. SHIRATANI). SEIENCE UNIV. OF TOKYO. 1-327 (1986)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] KATAYAMA, S. AND 20 OTHERS: "ON THE CLASS NUMBER OF TORUS, AND 20 OTHER ARTICLES" REPORTS OF THE 33TH SYMPOSIUM OF ALGEBRA (EDITED BY K. SHIRATANI). FUKUI UNIV.1-338 (1987)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] KADO, J. AND 14 OTHERS: "PSEUDO-RANK FUNCTIONS ON CROSSED PRODUCTS OF FINITE GROUPS OVER REGULAR RINGS,AND 13 OTHER ARTICLES" PROCEEDINGS OF THE 18TH SYMPOSIUM ON RING THEORY (EDITED BY K. OSIRO). YAMAGUCHI. 1-115 (1985)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] HIRATA, K. AND 13 OTHERS: "ON H-SEPARABILITY OF GROUP RINGS, AND 10 OTHER ARTICLES" PROCEEDINGS OF THE 19TH SYMPOSIUM ON RING THEORY. SHINSHU UNIV.1-106 (1986)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] MARUBAYASHI, H. UEDA, A. AND 17 OTHERS: "THE SKIN FORMAL POWER SERIES RINGS OVER TAME ORDERS IN SIMPLE ARTINIAN RING,AND 14 OTHER ARTICLES" PROCEEDINGS OF THE 20TH SYMPOSIUM ON RING THEORY (EDITED BY H. MARUYAMASHI). OKAYAMA UNIV.1-145 (1987)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] TANIZAKI, T. AND 15 OTHERS: "D-MODULES AND REPRESENTATION OF AFFINE WEYL GROUPS,AND 15 OTHER ARTICLES" REPORTS OF THE SYMPOSIUM ON THE REPRESENTATION OF ALGERAIC GROUP,LIE ALGEBRA HOPE ALGEBRA AND GALOIS THEORY (EDITED BY E. ABE). OSAKA UNIV.1-268 (1986)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] YAMAGATA, K. AND 8 OTHERS: "INTRODUCTION TO THE REPESENTATION THEORY OF ALGEBRAS,AND 8 OTHER ARTICLES" REPORTS OF THE SYMPOSIUM ON THE REPRESENTATION THEORY OF ALGEBRAS (EDITED BY H.TACHIKAWA). NARA. 1-235 (1986)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] SHOJI, K. AND 19 OTHERS: "SOME EXAMPLES OF SEMIGROUPS WHICH ARE AMALGAMATION BASES,AND 14 OTHER ARTICLES" PROCEEDINGS OF THE 10TH SYMPOSIUM ON SEMIGROUPS. JOSEI UNIV.1-83 (1986)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] OZEKI,M. AND 4 OTHERS: "APPLICATION OF THETA SERIES WITH SPHERICAL FUNCTIONS TO QUADRATIC FORMS, AND 4OTHER ARTICLES" PROTOCOL OF THE SYMPOSIUM ON NUMBER THEORY (EDITED BY K. SHIRATANI). KYUSHU UNIV.1-37 (1986)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] ITO, N. AND 21 OTHERS: "ON CODE THEORY, AND 17 OTHER ARTICLES" REPORTS ON THE ALGEBRAIC COMBINATORIAL THEORY (EDITED BY T. OYAMA). EHIME UNIV.1-168 (1986)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] MIKI, H. AND 14 OTHERS: "ON WEIL'S GROSSENCHARACTERS, AND 13 OTHER ARTICLES" REPORTS OF THE SYMPOSIUM ON NUMBER THEORY (EDITED BY Y. MORITA). NAGASAKI UNIV. 1-158 (1987)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] WAKAMATSU, T. AND 12 OTHERS: "DERIVED CATEGORIES IN THE REPRESENTATION THEORY OF ALGEBRAS, AND 12 OTHER ARTICLES" REPORTS OF THE SYNPOSIUM ON THE REPRESENTATION THEORY OF ALGEBRAS (EDITED BY K. YAMAGATA). NAGANO. 1-176 (1988)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] YOSHIDA, T. AND 10 OTHERS: "A MISTERY OF 24, AND 10 OTHER ARTICLES" REPORTS OF THE SYMPOSIUM ON DYNKIN MATHEMATICS (EDITED BY M. TAKEWUCHI). TSUKUBA UNIV.1-207 (1988)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] ODA, T.: CONVEX BODIES AND ALGEBRAIC GEOMETRY. SPRINGER-VERLAG, 280 (1987)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] KITAOKA, Y.: LECTURES ON SIEGEL MODULAR FORMS AND REPESENTATION BY QUADRATIC FORMS. SPRINGER-VERLAG, 227 (1986)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] 斎藤秀司他著,白谷克巳編: 第32回代数学シンポジウム報告集. 1-327 (1986)

    • Related Report
      1986 Annual Research Report
  • [Publications] 平田和彦他著,岩永恭雄編: POROCEEDINGS OF THE 19TH SYMPOSIUM ON RING THEORY. 1-106 (1986)

    • Related Report
      1986 Annual Research Report
  • [Publications] 伊藤昇他著,大山豪編: 代数的組合せ論報告集. 1-168 (1986)

    • Related Report
      1986 Annual Research Report
  • [Publications] 三木博雄他著,森田康夫編: 数論研究集会報告集. 1-158 (1987)

    • Related Report
      1986 Annual Research Report
  • [Publications] SHIRATANI,Katsumi: Advanced Studies in Pure Mathematics. (1987)

    • Related Report
      1986 Annual Research Report
  • [Publications] NAGATA,Masayoshi: Advanced Studies in Pure Mathematics. 11. (1987)

    • Related Report
      1986 Annual Research Report
  • [Publications] IWAHORI,Nagayoshi: Tokyo Journal of Mathematics. (1987)

    • Related Report
      1986 Annual Research Report
  • [Publications] TACHIKAWA,Hiroyuki: Journal of Algebra. 103. 662-676 (1986)

    • Related Report
      1986 Annual Research Report
  • [Publications] IHARA,Yasutaka: Annals of Mathematics. 123. 43-106 (1986)

    • Related Report
      1986 Annual Research Report
  • [Publications] IHARA,Yasutaka: Inventiones mathematicae. 86. 427-459 (1986)

    • Related Report
      1986 Annual Research Report
  • [Publications] IHARA,Yasutaka: Advanced Studies in Pure Mathematics. 12. (1987)

    • Related Report
      1986 Annual Research Report
  • [Publications] ODA,Tadao: Advanced Studies in Pure Mathematics. 8. 363-404 (1987)

    • Related Report
      1986 Annual Research Report
  • [Publications] ODA,Tadao: "Convex Bodies and Algebraic Geometry" Springer-Verlag, 280 (1987)

    • Related Report
      1986 Annual Research Report
  • [Publications] HOTTA,Ryoshi: "Introduction to D-modules" The Institute of Mathematical Sciences, 200 (1987)

    • Related Report
      1986 Annual Research Report
  • [Publications] 河田敬義: "ガウスの楕円関数論" 上智大学理工学部数学教室, 190 (1986)

    • Related Report
      1986 Annual Research Report
  • [Publications] KITAOKA,Yoshiyuki: "Lectures on Siegel Modular Forms and Representation by Quadratic Forms" Springer-Verlag, 227 (1986)

    • Related Report
      1986 Annual Research Report

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Published: 1987-03-30   Modified: 2016-04-21  

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