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2016 Fiscal Year Final Research Report

Study on the Picard groups of stable homotopy categories

Research Project

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Project/Area Number 26400092
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Geometry
Research InstitutionKochi 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
KeywordsHopkins’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

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Published: 2018-03-22  

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