Developement of Mathematics Arising from Generalization of Iwasawa Theory

2014 Fiscal Year Final Research Report

• Project/Area Number: 24654004
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Algebra
• Research Institution: Osaka University
• Principal Investigator: OCHIAI tadashi 大阪大学, 理学(系)研究科(研究院), 准教授 (90372606)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: Euler系 / 岩澤理論 / 肥田変形 / Selmer群

Outline of Final Research Achievements

In this research, we studied mainly (1) behaviour of mixed characteristic complete local rings under specialization (joint with Shimomoto), (2) Iwasawa Main Conjecture for Hilbert modular forms with complex multiplication (joint with Hara), (3) Coleman map for non ordinary Galois deformation (joint with Nuccio). For (1), we finished the first paper and it was recently accepted. We are now preparing the second paper which treats arithmetic applications of the first paper. For (2), we are now in the final revision of the first paper. For (3), we are trying to fill some missing details of the paper and we hope to finish the first paper soon.

Free Research Field

数論幾何学