Galois Descent Problem in Algebraic K-Theory

代数 K 理论中的伽罗瓦下降问题

• 批准号: 62540037
• 负责人: MASAHIKO NIWA
• 金额: $ 0.64万
• 依托单位: Shiga University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1987
• 资助国家: 日本
• 起止时间: 1987 至 1988
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-62540037/
• 关键词: G-category; O_G-category; Galois Descent; Fibered Category; 代数的K理論; 代数的K群; G-圏; ホモトピー極限問題

The notion of a category with an action of a group G - a G-category - is needed to make algebraic K-theory equivariant one. Though various notions have been used so far, the relations between these notions don't have been explained explicitly yet. I dealed uniformly with the notions of G-categories and established the comparison in the complete form by introducing the notion of a g-category from the point of view of galois descent in linear categories. It's important to consider simultaneously the limit categories together with G-categories and G-functors because of my philospohy "equivariant = Galois descent". The objects to appear are as follows.([.zu.])I also refer to exact G-categories and Q-construction induction theory etc.

需要具有 G 群作用的范畴的概念（G 范畴）才能使代数 K 理论等变。尽管到目前为止已经使用了各种概念，但这些概念之间的关系尚未得到明确解释。我统一处理了G范畴的概念，并从线性范畴的伽罗瓦下降的角度引入了g范畴的概念，建立了完整形式的比较。由于我的哲学“等变 = 伽罗瓦血统”，同时考虑极限类别以及 G 类别和 G 函子非常重要。出现的对象如下。([.zu.])我还参考了精确的G-范畴和Q-构造归纳理论等。

项目成果

Shiyo YAMAZOE: 滋賀大学教育学部紀要. 37. 1-7 (1987)

Shiyo YAMAZOE：滋贺大学教育学部通报，37. 1-7 (1987)。

Masahiko NIWA: "Lax colimits over abelian monoids and lax limits over groups (prearranged"

Masahiko NIWA：“阿贝尔幺半群的宽松余限和群的宽松限制（预先安排）”

丹羽雅彦: 数理科学講究録. 609. 61-75 (1987)

丹羽正彦：数学科学 609. 61-75 (1987)

Masahiko NIWA: 滋賀大学教育学部紀要. 38. (1988)

丹羽正彦：滋贺大学教育学部通报38。（1988）