Construction of the infinity-categories of mixed motives and mixed Tate motives by using the Bott periodicity

2016 Fiscal Year Final Research Report

• Project/Area Number: 26610010
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Algebra
• Research Institution: Ube National College of Technology
• Principal Investigator: Kato Yuki 宇部工業高等専門学校, 一般科, 講師 (50707130)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: 数論幾何学 / モデル圏 / 代数的K-理論 / A1ホモトピー論

Outline of Final Research Achievements

We established the theory of motivic derived algebraic geometry for left proper combinatorial simlicial model categories. In the framework of motivic derived algebraic geometry, we can construct of the motivic version of derived schemes and stacks by using motivic versions of infinity-categories. For example, we can obtain the moduli stacks of vector bundles and Thom spaces on motivic schemes. These results give us examples of applications of motivic derived algebraic geometry to moduli problems. We wrote the research the article "Motivic model categories and motivic derived algebraic geometry".

Free Research Field

代数学