| 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)
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| 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
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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
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