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Study of unramified extensions, with emphasis on Jacobian problem

Research Project

Project/Area Number 14540031
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

TSUCHIMOTO Yoshifumi (2003)  Kochi University, Faculty of science, assistant, 理学部, 助手 (10271090)

小駒 哲司 (2002)  高知大学, 理学部, 教授 (20127921)

Co-Investigator(Kenkyū-buntansha) FUKUMA Yoshiaki  Kochi University, Faculty of science, assistant professor, 理学部, 助教授 (20301319)
土基 善文  高知大学, 理学部, 助手 (10271090)
Project Period (FY) 2002 – 2003
Project Status Completed (Fiscal Year 2003)
Budget Amount *help
¥2,600,000 (Direct Cost: ¥2,600,000)
Fiscal Year 2003: ¥1,400,000 (Direct Cost: ¥1,400,000)
Fiscal Year 2002: ¥1,200,000 (Direct Cost: ¥1,200,000)
Keywordsunramified extension / Jacobian problem / Dixmier conjecture / p-curvature / algebraic variet / polarized variety / delta genus / arithmetic genus / 代数多根体 / デルタ極数 / Jacobian / 単純拡大 / conductor / Dixmire予想 / Weyl代数の自己準同型 / Weyl代数の中心 / Sympletic構造
Research Abstract

(1)We show that a Weyl algebra of positive characteristics is related to a matrix bundle on a affine space, and that we may obtain a process which is a 'inversion' of the 'geometric quantization' for this object.
(2)Using ultra filter on Spec(Z), we construct a field Qu of characteristic 0. We showed that an algebra endomorphism of Weyl algebra over Qu corresponds to an symplectic morphism of affine space.
(3)We show Dixmier conjecture may be deduced to Jacobian conjecture.
(4)Ultra filter limit of Cartier operator gives a new integration theory. It gives an important step to the Jacobian problem.
(5)We give a definition of the i-th sectional geometric genus and i-th delta genus of a generalized polarized manifold.
(6)We observe that the i-th sectional geometric genus and i-th delta genus have analogous properties to those of sectional genus and delta genus when the complete linear system |L| of L has no base point. We studied further what happens when |L| has some base points.
(7)We give a definition of the i-th sectional H-arithmetic genus _X^H_i(X,L) of a polarized manifold(X,L).
(8)Expecting that g_2(X,L) and _X^H_2(X,L)(resp.) are analogous to geometric genus and arithmetic genus _X(O)(resp.), we propose some problems on polarized manifold as an analogy to the known results on the theory of surface.

Report

(3 results)
  • 2003 Annual Research Report   Final Research Report Summary
  • 2002 Annual Research Report
  • Research Products

    (16 results)

All Other

All Publications (16 results)

  • [Publications] Y.Tsuchimoto: "Preliminaries on Dixmier conjecture"Mem.Fac.Sci.Kochi Univ.Ser.A Math.. 24. 43-59 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Fukuma: "A generalization of the sectional genus and the Δ-genus of polarized varieties."京都大学数理解析研究所講究録. 1345. 166-181 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Fukuma: "On the c_r-sectional geometric genus of generalized polarized manifolds."Japanese Journal of Mathematics. 29巻2号. 335-355 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Fukuma: "On the sectional geometric genus of quasi-polarized varieties, II."manuscripta mathematica. 113巻2号. 211-237 (2004)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Fukuma: "Problems on the second sectional invariants of polarized manifolds."Mem.Fac.Sci.Kochi Univ.Ser.A Math.. (印刷中). (2004)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Ysuchimoto: "Preliminaries on Dixmier conjecture"Mem.Fac.Sci.Kochi Uniy.Ser.A Math.. 24. 43-59 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Fukuma: "A generalization of the sectional genus and the Δ-genus of polarized varieties."RIMS Kokyuroku. 1345. 166-181 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Fukuma: "On the c_r-sectional geometric genus of generalized polarized manifolds."Japanese Journal of Mathematics. 29(2). 335-355 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Fukuma: "On the sectional geometric genus of quasi-polarized varieties, II."manuscripta mathematica. 113(2). 211-237 (2004)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Fukuma: "Problems on the second sectional invariants of polarized manifolds."Mem.Fac.Sci.Kochi Uniy.Ser.A Math.. (in print). (2004)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Tsuchimoto: "Preliminaries on Dixmier conjecture"Mem.Fac.Sci.Kochi Univ.Ser.A Math.. 24. 43-59 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Y.Fukuma: "A generalization of the sectional genus and the Δ-genus of polarized Varieties."京都大学数理解析研究所講究録. 1345. 166-181 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Y.Fukuma: "On the c_r-sectional geometric genus of generalized polarized manifolds."Japanese Journal of Mathematics. 29巻2号. 335-355 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Y.Fukuma: "On the sectional geometric genus of quasi-polarized varieties, II."manuscripta mathematica. 113巻2号. 211-237 (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] Y.Fukuma: "Problems on the second sectional invariants of polarized manifolds."Mem.Fac.Sci.Kochi Univ.Ser.A Math.. (印刷中). (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] Y.Tsuchimoto: "Preliminaries on Dixmier conjecture"Mem. Fac. Sci. Kochi Univ. Ser. A (Math.). 24. 43-59 (2003)

    • Related Report
      2002 Annual Research Report

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Published: 2002-04-01   Modified: 2016-04-21  

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