Studies of the structure of module categories, derived categories and singularity categories of commutative rings
| Project/Area Number |
25400038
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | Nagoya University |
|---|
Principal Investigator |
Takahashi Ryo 名古屋大学, 多元数理科学研究科, 准教授 (40447719)
|
|---|
| Project Period (FY) |
2013-04-01 – 2016-03-31
|
| Project Status |
Completed (Fiscal Year 2015)
|
| Budget Amount *help |
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2013: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
|
|---|
| Keywords | 可換環の表現論 / 加群圏 / 導来圏 / 特異圏 / 分解部分圏 / 特異点 / Ext関手 / Rouquier次元 / 孤立特異点 / thick部分圏 / Cohen-Macaulay環 / Cohen-Macaulay加群 / Gorenstein環 |
|---|
| Outline of Final Research Achievements |
I did several researches in the representation theory of commutative rings. More precisely, for a given commutative noetherian ring, I investigated the structure of the module category (i.e., the category of finitely generated modules), the (bounded) derived category and the singularity category. As main achievements, I obtained complete classification of the resolving subcategories of the module category of a complete intersection ring. Also, using the dimension and radius of a subcategory of the module category, I explored certain properties of singularities. Furthermore, I studied annihilation of the Ext functor, and related it to generation of the derived and singularity categories, especially to the Rouquier dimension.
|
Report
(4 results)
Research Products
(65 results)
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
[Presentation] TBD2017
Author(s)
Ryo Takahashi
Organizer
MSRI Summer Graduate School
Place of Presentation
Okinawa Institute of Science and Technology Graduate University (OIST)
Year and Date
2017-05-22
Related Report
Int'l Joint Research / Invited
-
[Presentation] TBD2016
Author(s)
Ryo Takahashi
Organizer
17th Workshop and International Conference on Representations of Algebras (ICRA)
Place of Presentation
Syracuse University, Syracuse NY, USA
Year and Date
2016-08-10
Related Report
Int'l Joint Research / Invited
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
[Presentation] Generating singularity categories
Author(s)
Ryo Takahashi
Organizer
Commutative Algebra and its interaction to Algebraic Geometry and Combinatorics
Place of Presentation
Institute of Mathematics, Hanoi, Vietnam
Related Report
Invited
-
-
