Research on integral closure and related topics

• Project/Area Number: 21540046
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Algebra
• Research Institution: Tokyo Metropolitan University
• Principal Investigator: KAWASAKI Takesi 首都大学東京, 理工学研究科, 助教 (40301410)
• Project Period (FY): 2009 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000); Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
• Keywords: 正準現予想 / 改良新交差予想 / 単項式予想 / 直和因子予想 / シジジー予想 / 正準元予想 / 整閉包 / Artin-Rees定理 / ホモロジカル予想 / Briancon-Skoda定理

Research Abstract

We obtain a new characterization of the canonical element conjecture, which is a most important one among homological conjectures, and give new other proofs of known partial results about it. Furthermore, we obtain a new sufficient condition using a p-standard system of parameters.