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On the deformations of cyclic Galoi coverings of algebraic curves

Research Project

Project/Area Number 62540066
Research Category

Grant-in-Aid for General Scientific Research (C)

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

Principal Investigator

SEKIGUCHI Tsutomu  Chuo Univ., Dept. of Math., Professor, 理工学部, 教授 (70055234)

Co-Investigator(Kenkyū-buntansha) MATSUYAMA Yoshio  Chuo Univ., Dept. of Math., Professor, 理工学部, 教授 (70112753)
ISHII Hitoshi  Chuo Univ., Dept. of Math., Professor, 理工学部, 教授 (70102887)
IWANO Masahiro  Chuo Univ., Dept. of Math., Professor, 理工学部, 教授 (70087013)
KURIBAYASHI Akikazu  Chuo Univ., Dept. of Math., Professor, 理工学部, 教授 (40055033)
SEKINO Kaoru  Chuo Univ., Dept. of Math., Professor, 理工学部, 教授 (40054994)
三松 佳彦  中央大学, 理工学部, 専任講師 (70190725)
百瀬 文之  中央大学, 理工学部, 助教授 (80182187)
Project Period (FY) 1987 – 1989
Project Status Completed (Fiscal Year 1989)
Budget Amount *help
¥2,400,000 (Direct Cost: ¥2,400,000)
Fiscal Year 1989: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 1988: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 1987: ¥800,000 (Direct Cost: ¥800,000)
KeywordsWitt group / Artin-Schreier / Kummer / Algebraic curve / Extension / Group scheme / 群スキーム / 群スキームの拡大 / N〓ron blow-up
Research Abstract

Our aim of this research is to construct a lifting of a couple (C,sigma) of a complete non-singular curve C over a field of characteristic p (>O), and its automorphism sigma of order p^n (n<greater than or equal>1). For the case of n = 1, we have obtained an affirmative result by using Lang's class field theory. In the argument, one of the important ideas if to construct a deformation of the Artin-Schreier theory to the Kummer theory, i.e., to construct a deformation of an additive group to a multiplicative group. Therefore when we try to solve the problem for n<greater than or equal>2, first of all, we must construct the deformations of the Witt group W_n to a torus (G_m)^n. We decided Completely such deformations for n=2 in 1988 and 1989. In 1990, we discovered a vanishing theorem for extensions of additive groups by a torus over an Artin local ring, and usinit we treated the extensions of group schemes over a Artin local ring. Moreover, by using the vanishing theorem, we succeeded in constructing the deformations of the Artin-Schreier-Witt exact sequence to an exact sequence of Kummer type. In future, we must construct a unified theory of the Artin-Schreier-Witt and the Kummer theories, and apply it to our original problem.

Report

(4 results)
  • 1989 Annual Research Report   Final Research Report Summary
  • 1988 Annual Research Report
  • 1987 Annual Research Report
  • Research Products

    (27 results)

All Other

All Publications (27 results)

  • [Publications] "How coarse the coarse moduli spaces for curves are!" Algebraic Geometry and Commutative Algebra. 693-712 (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] "On the deformation of Artin-Schreier to Kummer" Ann.scient.Ec.Norm.Sup.22. 345-375 (1989)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] "On the deformations of Witt groups to tori II" Chuo-Math.Preprint Series,(J.Alg.). 1. (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] "A case of extension of group schemes over a discrete valuation ring" Chuo-Math.Preprint Series,(Tsukuba J.). 5. (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] "Some cases of extensions of group schemes over a discrete valuation ring I" Chuo-Math.Preprint Series. 8. (1989)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] "Some cases of extensions of group schemes over a discrete valuation ring II" Bull.Facul.Sci.& Eng.Chuo University. 32. 17-35 (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] T. Sekiguchi: "How coarse the coarse moduli space of curves are!" Alg. and Comm. Alg. in Honor of M. Nagata, 693-712(1987).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] K. Sekino: "On the fields of definition for a curve and its Jacobian variety" Bull. Facul. Sci. & Eng. Chuo Univ., 31, 29-31(1988).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] T. Sekiguchi: "On the deformation of Artin-Schreier to Kummer" Ann. scient. Ec. Norm. Sup., 22, 345-375(1989).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] T. Sekiguchi: "On the deformations of Witt groups to tori II" Chuo-Math. Preprint Series 1, 1988; J. Alg.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] T. Sekiguchi: "A case of extensions of group schemes over a discrete valuation ring" Chuo-Math. Preprint Series 5, 1988; Tsukuba J.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] T. Sekiguchi: "Some cases of extensions of group schemes over a discrete valuation ring I" Chuo-Math. Preprint Series 8, 1989.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] T. Sekiguchi: "Some cases of extensions of group schemes over a discrete valuation ring II" Bull. Facul. Sci. & Eng. Chuo Univ. 32, 17-35(1990).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] "How coarse the coarse moduli spaces for curves are!" Algebraic Geometry and Commutative Algebra. 693-712 (1987)

    • Related Report
      1989 Annual Research Report
  • [Publications] "On the deformation of Artin-Schreier to Kummer" Ann.scient.Ec.Norm.Sup. 22. 345-375 (1989)

    • Related Report
      1989 Annual Research Report
  • [Publications] "On the deformations of Witt groups to tori II" Chuo-Math.Preprint Series. 1. (1988)

    • Related Report
      1989 Annual Research Report
  • [Publications] "A case of extensions of group schemes over a discrete valuatin ring" Chro-Math.Preprint Series. 5. (1988)

    • Related Report
      1989 Annual Research Report
  • [Publications] "Some cases of extensions of group schemes over a discrete valuation ring I" Chuo-Math.Preprint Series. 8. (1989)

    • Related Report
      1989 Annual Research Report
  • [Publications] "Some cases of extenstions of group schemes over a discrete valuation ring II" Bull.Facul.sci.& Eng.Chuo University. 32. 17-35 (1990)

    • Related Report
      1989 Annual Research Report
  • [Publications] 関口力: Algebroic geometry and commutative algebra in Honor of Masayoshi Nagata. 693-712 (1987)

    • Related Report
      1988 Annual Research Report
  • [Publications] 関口力: Ann.Sci.Ec.Norm.Sup.

    • Related Report
      1988 Annual Research Report
  • [Publications] 関口力: Algebraic and topological theories to the memory of Dr.Miyata. 283-298 (1985)

    • Related Report
      1988 Annual Research Report
  • [Publications] 関口力: Chuo Univ.Preprint series No.1.(1988)

    • Related Report
      1988 Annual Research Report
  • [Publications] 関口力: Chuo Univ.Preprint series No.5.(1988)

    • Related Report
      1988 Annual Research Report
  • [Publications] 関口 力: Algebraie Geometry and Comnutative Algebra in Honor of Masayoshi Nagata. 101-120 (1987)

    • Related Report
      1987 Annual Research Report
  • [Publications] 栗林 泉: Tsukuba J.Math.11. 287-301 (1987)

    • Related Report
      1987 Annual Research Report
  • [Publications] F.Oort: J.Math.Soc.Japan. 38. 427-437 (1986)

    • Related Report
      1987 Annual Research Report

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Published: 1987-04-01   Modified: 2016-04-21  

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