Period map of the moduli space of categories and derived geometry

2021 Fiscal Year Final Research Report

• Project/Area Number: 17K14150
• 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): 2017-04-01 – 2022-03-31
• Keywords: 安定無限圏 / ホッホシルトホモロジー / 変形理論 / 周期写像 / 導来代数幾何

Outline of Final Research Achievements

In this research project, I have studied the Hpdge-theoretic invariants arising from a family of stable infinity-categorties. I would like to summerize the resluts which I obtained. Let us conisder the Hochschild pair. I gave a conceptual and simple constructuon of the algberaic structure on the Hochschild pair associated to a stable infinity-category. Moreover, I discovered the moduli-theoretic interpretation of this algebraic structure on the Hochschild pair.
I have constructed D-module structure on the periodic cyclic homology arising from a family of stable infinity-categories. I discovered two methods.
The first method is an application of the Hochshicla pair. The second method is to use the canonical extension of factorization homology.

Free Research Field

代数幾何

Academic Significance and Societal Importance of the Research Achievements

周期写像を圏に拡張することで様々な出自の圏をして統合し、ホッジ理論的な考察ができ圏論的なミラー対称性などにも応用があると考えられる。また、大局的にはバラバラになりがちな数学の分野を統合するための一助になり数学の専門外のひとにも数学を身近にする効果があると考えられる。