Study on the Picard groups of stable homotopy categories

2016 Fiscal Year Final Research Report

• Project/Area Number: 26400092
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Kochi University
• Principal Investigator: Shimomura Katsumi 高知大学, 教育研究部自然科学系理学部門, 教授 (30206247)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: Hopkinｓ’Picard group / 安定ホモトピー圏 / Morava K-theory / Johnson-Wilson spectrum / Adams スペクトル系列

Outline of Final Research Achievements

The stable homotopy category of spectra is understood by the stable homotopy categories K_n of spectra localized by the Morava K-theoreis K(n) for a non-negative integers n. To determine the Hopkins' Picard group of K_n is one of important problems in the stable homotopy theory. Our aim of this study is to consider the Picard groups not by the Morava K-theories, but by the Johnson-Wilson spectrum E(n). One of our main results is that the subgroup of the Picard group of K_n obtained by a geometric consideration is isomorphic to the counterpart of the Picard group of the stable homotopy category localized by E(n), under a condition.

Free Research Field

安定ホモトピー論