Prospects for Mordell-Weil Lattices and Algebraic Surfaces

2010 Fiscal Year Self-evaluation Report

• Project/Area Number: 20540051
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Algebra
• Research Institution: Rikkyo University
• Principal Investigator: SHIODA Tetsuji Rikkyo University, 理学部, 名誉教授 (00011627)
• Project Period (FY): 2008 – 2012
• Keywords: モーデル・ヴェイユ格子 / K3曲面 / 球のつめこみ / 整点 / グレブナ基底 / abc-定理

Research Abstract

以下のテーマを中心に研究、
(1)K3曲面と球のつめこみ問題、
(2)ある種の楕円曲面の存在、有限性定理と定義体の問題、(3)モーデル・ヴェイユ格子から生ずるガロア表現と代数方程式、(4)フェルマー曲面上の代数的サイクル、(5)楕円曲面の整点の研究とグレブナ基底

Research Products

• [Journal Article] R.van Luijk : Lines on Fermat surfaces (2010)
  • Author(s): M.Schuett, T.Shioda
  • Journal Title: Journal of Number Theory 130 Pages: 1939-1963
  • Peer Reviewed
• [Journal Article] Elliptic Surfaces : Advanced Studies in Pure (2010)
  • Author(s): M.Schuett, T.Shioda
  • Journal Title: Mathematics 60 Pages: 51-160
  • Peer Reviewed
• [Journal Article] Correction and supplement : Generators of the Neron-Severi group of a Fermat surface (2010)
  • Author(s): N.Aoki, T.Shioda
  • Journal Title: Comment.Math.Univ.St,Pauli 59 Pages: 65-75
  • Peer Reviewed
• [Journal Article] Groebner basis, Mordell- Weil lattices and deformation of singularities (2010)
  • Author(s): T.Shioda
  • Journal Title: I.Proc.Japan Acad. 86(A) Pages: 21-26
  • Peer Reviewed
• [Journal Article] Groebner basis, Mordell- Weil lattices and deformation of singularities (2010)
  • Author(s): T.Shioda
  • Journal Title: II.Proc.Japan Acad. 86(A) Pages: 27-32
  • Peer Reviewed
• [Journal Article] Some explicit integral polynomials with Galois group W(E_8) (2009)
  • Author(s): T.Shioda
  • Journal Title: Proc.Japan Acad. 85A Pages: 118-121
  • Peer Reviewed
• [Journal Article] K3 surfaces and sphere packings (2008)
  • Author(s): T.Shioda
  • Journal Title: J.Math.Soc.Japan 60 Pages: 1083-1105
  • Peer Reviewed
• [Journal Article] The abc-theorem, Davenport's inequality and elliptic surfaces (2008)
  • Author(s): T.Shioda
  • Journal Title: Proc.Japan Acad. 84A Pages: 51-56
  • Peer Reviewed
• [Presentation] Remarkable configurations of curves on K3 by Dolgachev- Kondo- Katsura (2011)
  • Author(s): T.Shioda
  • Organizer: Workshop on Arithmetic and Algebraic Geometry
  • Place of Presentation: 東京大学(招待講演)
  • Year and Date: 2011-01-19
• [Presentation] Excellent families of rational elliptic surfaces (2010)
  • Author(s): T.Shioda
  • Organizer: Workshop on Reflection Groups,Lattices and Algebraic Geometry
  • Place of Presentation: 名古屋大学(招待講演)
  • Year and Date: 2010-11-24
• [Presentation] Mordell-Weil lattices and Galois representations : old and new (2010)
  • Author(s): T.Shioda
  • Organizer: Workshop on Arithmetic on Surfaces
  • Place of Presentation: Lorentz Center, Leiden Univ(招待講演)
  • Year and Date: 2010-10-25
• [Presentation] Cubic surfaces via Mordell-Weil lattice revisited (2010)
  • Author(s): T.Shioda
  • Organizer: Workshop on Elliptic fibrations and K3 surfaces
  • Place of Presentation: Humboldt Univ Berlin(招待講演)
  • Year and Date: 2010-07-14
• [Presentation] Some Topics on Mordell-Weil lattices (2009)
  • Author(s): T.Shioda
  • Organizer: 代数学セミナー
  • Place of Presentation: 埼玉大学(招待講演)
  • Year and Date: 2009-09-15
• [Presentation] Mordell-Weil lattices and Galois representations (2009)
  • Author(s): T.Shioda
  • Organizer: 日本数学会・代数学シンポジウム
  • Place of Presentation: 明治大学(招待講演)
  • Year and Date: 2009-08-04
• [Presentation] Mordell--Weil lattices and integral sections (2009)
  • Author(s): T.Shioda
  • Organizer: Conference "Diophantine Geometry : into the Millenniumm"
  • Place of Presentation: ETH-Zurich.(招待講演)
  • Year and Date: 2009-06-05
• [Book] abc-定理,楕円曲面,モーデル・ヴェイユ格子(東京大学数理科学レクチャーノート4) (2008)
  • Author(s): 塩田徹治
  • Total Pages: 78
  • Publisher: 東京大学大学院数理科学研究科