Derived geometry and duality

2016 Fiscal Year Final Research Report

• Project/Area Number: 25800001
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Algebra
• Research Institution: Tohoku University
• Principal Investigator: Iwanari Isamu 東北大学, 理学研究科, 准教授 (70532547)
• Project Period (FY): 2013-04-01 – 2017-03-31
• Keywords: 淡中双対 / 高次圏 / モチーフ / DG代数 / 変形理論

Outline of Final Research Achievements

The principal purpose of this program is to study a duality of tannakian type for higher categories and to apply it to various theory such as mixed motives. I proved a tannakian characterization theorem for symmetric monoidal stable infinity-categories that satisfy a certain simple condition (so-called fine tannakian infinity-categories). I applied this theory to mixed motives to obtain motivic Galois stacks and associated motivic Galois group. I also define a motivic rational homotopy type and its relation with motivic Galois actions and related notions. I applied the tannaka duality theory to motivic rational homotopy types.

Free Research Field

代数幾何学