Study of affine fibrations

• Project/Area Number: 24540037
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: University of Fukui
• Principal Investigator: Onoda Nobuharu 福井大学, 工学(系)研究科(研究院), 教授 (40169347)
• Research Collaborator: Bhatwadekar S. M. Bhaskaracharya Pratishthana, 教授 ; Dutta A. K. Indian Statistical Institute, 教授
• Project Period (FY): 2012-04-01 – 2016-03-31
• Project Status: Completed (Fiscal Year 2015)
• Budget Amount: ¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000); Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2012: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
• Keywords: 代数学 / 可換環論 / アフィン代数幾何学 / 国際研究者交流 / インド

Outline of Final Research Achievements

Some results are obtained regarding affine fibration which is an important subject both in commutative algebra and affine algebraic geometry. In particular, fibre conditions are given for algebras A to be finitely generated over a two dimensional regular local ring R, and examples are constructed to show the necessity of the conditions. Moreover conditions are given for the equivalence between the class of algebras generated by idempotents and the class of algebras which are quotients of group algebras of commutative groups.

Research Products

• [Int'l Joint Research] Indian Statistical Institute/Bhaskaracharya Pratishthana(India)
• [Journal Article] Commutative rings over which algebras generated by idempotents are quotients of group algebras (2015)
  • Author(s): Hideyasu Kawai and Nobuharu Onoda
  • Journal Title: Journal of Commutative Algebra Volume: 7 Issue: 3 Pages: 373-391
  • DOI: 10.1216/jca-2015-7-3-373
  • Peer Reviewed
• [Journal Article] On algebras which are locally A^1 in codimension-one (2013)
  • Author(s): S.M.Bhatwadekar, A.K.Dutta, Nobuharu Onoda
  • Journal Title: Transactions of The American Mathematical Society Volume: 365 Pages: 4497-4537
  • Peer Reviewed
• [Presentation] Poincare series of the kernel of a locally nilpotent derivation on the polynomial ring (2014)
  • Author(s): Nobuharu Onoda
  • Organizer: アフィン代数幾何学研究シンポジウム
  • Place of Presentation: 首都大学東京
  • Year and Date: 2014-09-14
  • Invited
• [Presentation] On finite generation of algebras over two-dimensional regular local rings (2013)
  • Author(s): 小野田信春
  • Organizer: 第11回アフィン代数幾何学研究集会
  • Place of Presentation: 関西学院大学大阪梅田キャンパス
  • Invited