Applications of homological category theory to algebraic geometry and representation theory

同调范畴论在代数几何和表示论中的应用

• 批准号: 22740005
• 负责人: HIROYUKI Nakaoka
• 金额: $ 1.83万
• 依托单位: Kagoshima University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2010
• 资助国家: 日本
• 起止时间: 2010 至 2012
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22740005/
• 关键词: 三角圏; Mackey 関手; アーベル圏; 丹原関手; Mackey関手; biset; クラスター傾; 2-cateory; Burnside環

(I) Homological structures on triangulated categories: Torsion pair on a triangulated category generalizes simultaneously ‘t-structure’, a well-known classical notion which is also important in algebraic geometry, and ‘cluster tilting subcategory’, which is formulated recently in representation theory of algebras. While investigating algebraic structures ontorsion pairs, we have given a construction which associates an abelian category to each torsion pair, which generalizes the heart of a t-structure and the cluster tilting quotient.(II) Bivariant functors associated to finite groups: We are investigating ‘Mackey functor’ ‐a functor bivariant on afinite group, and especially ‘Tambara functor’, which plays a role of commutativering in Mackey functor theory, from a categorical point of view. As a bivariant analog of commutative ring theory, we have formulated fundamental operations on Tambara functors, corresponding to ideal quotient, fraction, polynomial and primespectrum.

(I) 三角范畴上的同调结构：三角范畴上的扭转副同时概括了“t-结构”（一个众所周知的经典概念，在代数几何中也很重要）和“簇倾斜子范畴”（最近在表示中提出）在研究代数结构扭转对时，我们给出了一种将阿贝尔范畴与每个扭转对相关联的构造，它概括了t-结构和簇倾斜商。（II）与有限群相关的双变函子：我们正在研究“Mackey函子”——有限群上的双变函子，特别是“Tambara函子”，它在Mackey函子中起着交换环的作用理论，从范畴的角度来看，作为交换环理论的二变类比，我们制定了与理想相对应的 Tambara 函子的基本运算。商、分数、多项式和素谱。

项目成果

Spectrum of the Burnside Tambara functor on a cyclic $p$-group

循环 $p$ 群上 Burnside Tambara 函子的谱

• 作者: A. Tanaka and Y. Kamishima;與倉昭治;Hiroyuki Nakaoka;Shoji Yokura;Hiroyuki Nakaoka;Hiroyuki Nakaoka;H. Tsuji;Jenizon and Tadashi Aikou;H.Tsuji;Tadashi Aikou and Haripamyu;H. Tsuji;Hiroyuki Nakaoka;H. Tsuji;H. Tsuji;Hiroyuki Nakaoka;Ｈａｊｉｍｅ Ｔｓｕｊｉ;Hiroyuki Nakaoka;Hajime Tsuji;Hiroyuki Nakaoka;Hajime Tsuji;Tadashi Aikou;Hajime Tsuji;Hajime TSUJI;Hiroyuki Nakaoka;辻 元;Shoji Yokura and Joerg Schuermann;辻 元;辻 元;Hiroyuki Nakaoka;Hiroyuki Nakaoka;S. Yokura;S. Yokura;宮嶋公夫;K. Miyajima;K. Miyajima;Tadashi Aikou;Tadashi Aikou;Shoji Yokura;Shoji Yokura;Shoji Yokura;與倉昭治;Tadashi Aikou;Hiroyuki Nakaoka;Hiroyuki Nakaoka;Hiroyuki Nakaoka
• 通讯作者: Hiroyuki Nakaoka

Some homological constructions on triangulated categories

三角范畴的一些同调构造

• 发表时间: 2011
• 作者: Noriyuki Abe;Hiroyuki Nakaoka;Hiroyuki Nakaoka;Hiroyuki Nakaoka;Hiroyuki Nakaoka;Hiroyuki Nakaoka;Hiroyuki Nakaoka;Hiroyuki Nakaoka
• 通讯作者: Hiroyuki Nakaoka

General Heart Construction on a Triangulated Category (II): Associated Homological Functor

• DOI: 10.1007/s10485-010-9226-z
• 发表时间: 2009-10
• 期刊: Applied Categorical Structures
• 影响因子: 0.6
• 作者: N. Abe;H. Nakaoka

On torsion pairs on triangulated categories

关于三角类别上的扭转副

• 作者: A. Tanaka and Y. Kamishima;與倉昭治;Hiroyuki Nakaoka;Shoji Yokura;Hiroyuki Nakaoka;Hiroyuki Nakaoka;H. Tsuji;Jenizon and Tadashi Aikou;H.Tsuji;Tadashi Aikou and Haripamyu;H. Tsuji;Hiroyuki Nakaoka;H. Tsuji;H. Tsuji;Hiroyuki Nakaoka;Ｈａｊｉｍｅ Ｔｓｕｊｉ;Hiroyuki Nakaoka;Hajime Tsuji;Hiroyuki Nakaoka;Hajime Tsuji;Tadashi Aikou;Hajime Tsuji;Hajime TSUJI;Hiroyuki Nakaoka;辻 元;Shoji Yokura and Joerg Schuermann;辻 元;辻 元;Hiroyuki Nakaoka;Hiroyuki Nakaoka;S. Yokura;S. Yokura;宮嶋公夫;K. Miyajima;K. Miyajima;Tadashi Aikou;Tadashi Aikou;Shoji Yokura;Shoji Yokura;Shoji Yokura;與倉昭治;Tadashi Aikou;Hiroyuki Nakaoka;Hiroyuki Nakaoka
• 通讯作者: Hiroyuki Nakaoka

Some algebraic operations on Tambara functors on finite groups

有限群上 Tambara 函子的一些代数运算

• 发表时间: 2012
• 作者: Noriyuki Abe;Hiroyuki Nakaoka;Hiroyuki Nakaoka;Hiroyuki Nakaoka;Hiroyuki Nakaoka;Hiroyuki Nakaoka;Hiroyuki Nakaoka
• 通讯作者: Hiroyuki Nakaoka