Study of polynomial rings using higher derivations

2015 Fiscal Year Final Research Report

• Project/Area Number: 24740022
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Algebra
• Research Institution: Tokyo Metropolitan University
• Principal Investigator: Kuroda Shigeru 首都大学東京, 理工学研究科, 教授 (70453032)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Keywords: 多項式環 / 正標数 / 高階導分 / 局所冪零導分 / 多項式自己同型 / 線形化問題 / 安定座標 / アフィン代数幾何学

Outline of Final Research Achievements

Many of the basic problems in polynomial ring are still unsolved, and are studied systematically as difficult problems in Commutative Ring Theory or Algebraic Geometry. In the study of polynomial rings, techniques based on degrees and derivations are effective, but are often not applicable to positive characteristic cases. In this research, we used "higher derivations" effectively in addition to the previous techniques. We studied wide range of problems in polynomial rings including positive or arbitrary characteristic cases, and obtained various new results.

Free Research Field

多項式環論，アフィン代数幾何学