A New Approach to the Classification of Local Rings via Deviations from Gorensteinness

Research Project

Project/Area Number	25K06941
Research Category	Grant-in-Aid for Scientific Research (C)
Allocation Type	Multi-year Fund
Section	一般
Review Section	Basic Section 11010:Algebra-related
Research Institution	Meiji University
Principal Investigator	松岡直之明治大学, 理工学部, 専任教授 (80440155)
Project Period (FY)	2025-04-01 – 2028-03-31
Project Status	Granted (Fiscal Year 2025)
Budget Amount *help	¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000) Fiscal Year 2027: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000) Fiscal Year 2026: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000) Fiscal Year 2025: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywords	almost Gorenstein環 / nearly Gorenstein環 / Cohen-Macaulay環 / Gorenstein環 / 数値半群環
Outline of Research at the Start	本研究は，Cohen-Macaulay 局所環を正準加群の構造を通してGorenstein性との差異に着目し，almost Gorenstein 性および nearly Gorenstein 性の比較・融合・一般化を通じて，環の新たな階層的分類理論を構築することを目的とする。数値半群環を基本モデルとし，まずは 1 次元での精密な解析を進め，その成果をもとに高次元への拡張を図る。