Galois Descent Problem in Algebraic K-Theory

Research Project

Project/Area Number	62540037
Research Category	Grant-in-Aid for General Scientific Research (C)
Allocation Type	Single-year Grants
Research Field	代数学・幾何学
Research Institution	Shiga University
Principal Investigator	MASAHIKO NIWA Shiga University, Faculty of Education, Associate Professor, 教育学部, 助教授 (00024969)
Co-Investigator(Kenkyū-buntansha)	SHIRO YAMAZOE Shiga University, Faculty of Education, Associate Professor, 教育学部, 助教授 (10075137)
Project Period (FY)	1987 – 1988
Project Status	Completed (Fiscal Year 1988)
Budget Amount *help	¥1,000,000 (Direct Cost: ¥1,000,000) Fiscal Year 1988: ¥500,000 (Direct Cost: ¥500,000) Fiscal Year 1987: ¥500,000 (Direct Cost: ¥500,000)
Keywords	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
Research Abstract	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.