On the Picard group graded homotopy groups of a finite type two $K(2)$-local spectrum at the prime three

IF 0.8 4区数学 Q2 MATHEMATICS

Homology Homotopy and Applications Pub Date : 2022-01-01 DOI:10.4310/hha.2022.v24.n1.a10

Ippei Ichigi, K. Shimomura

引用次数: 0

Abstract

. Consider Hopkins’ Picard group of the stable homotopy category of E (2)-local spectra at the prime three, consisting of homotopy classes of invertible spectra [1]. Then, it is isomorphic to the direct sum of an in(cid:12)nite cyclic group and two cyclic groups of order three. We consider the Smith-Toda spectrum V (1) and the co(cid:12)ber V 2 of the square (cid:11) 2 of the Adams map, which is a ring spectrum. In this paper, we introduce imaginary elements which make computation clearer, and determine the module structures of the Picard group graded homotopy groups (cid:25) ⋆ ( V (1)) and (cid:25) ⋆ ( V 2 ).

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有限型Picard群的二阶K(2)$-局域谱

．考虑由可逆谱[1]的同伦类组成的E(2)的稳定同伦范畴的Hopkins ' Picard群。然后，它同构于一个in(cid:12)非环群与两个3阶环群的直和。我们考虑Smith-Toda谱V(1)和Adams图的正方形(cid:11) 2的co(cid:12)ber V(2)，这是一个环谱。本文引入虚元使计算更加清晰，并确定了Picard群梯度同伦群(cid:25) - - (V(1))和(cid:25) - - (v2)的模结构。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Homology Homotopy and Applications 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Homology, Homotopy and Applications is a refereed journal which publishes high-quality papers in the general area of homotopy theory and algebraic topology, as well as applications of the ideas and results in this area. This means applications in the broadest possible sense, i.e. applications to other parts of mathematics such as number theory and algebraic geometry, as well as to areas outside of mathematics, such as computer science, physics, and statistics. Homotopy theory is also intended to be interpreted broadly, including algebraic K-theory, model categories, homotopy theory of varieties, etc. We particularly encourage innovative papers which point the way toward new applications of the subject.