等变稳定同伦中的粉碎局域化

IF 0.5 4区数学

Journal of Homotopy and Related Structures Pub Date : 2022-07-15 DOI:10.1007/s40062-022-00310-1

Christian Carrick

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引用次数: 6

摘要

研究了在各种等变函子下，粉碎Bousfield定域的行为。我们证明了实Johnson-Wilson理论\(E_{\mathbb {R}}(n)\)的粉碎积和色收敛定理的类似物只有在Borel完备后才成立。我们为Beaudry, Hill, Shi和Zeng构建的\(C_{2^n}\) -等变Johnson-Wilson理论建立了类似的结果。我们证明了诱导定位升级了\(N_\infty \) -代数的可用规范，并确定了出现哪些新规范。最后，我们在\(E_\infty \) -环的拟伽罗瓦扩展的背景下探讨了粉碎局域化结果的推广。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Smashing localizations in equivariant stable homotopy

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Smashing localizations in equivariant stable homotopy

We study how smashing Bousfield localizations behave under various equivariant functors. We show that the analogs of the smash product and chromatic convergence theorems for the Real Johnson–Wilson theories \(E_{\mathbb {R}}(n)\) hold only after Borel completion. We establish analogous results for the \(C_{2^n}\)-equivariant Johnson–Wilson theories constructed by Beaudry, Hill, Shi, and Zeng. We show that induced localizations upgrade the available norms for an \(N_\infty \)-algebra, and we determine which new norms appear. Finally, we explore generalizations of our results on smashing localizations in the context of a quasi-Galois extension of \(E_\infty \)-rings.

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来源期刊

Journal of Homotopy and Related Structures Mathematics-Geometry and Topology

自引率

0.00%

发文量

期刊介绍： Journal of Homotopy and Related Structures (JHRS) is a fully refereed international journal dealing with homotopy and related structures of mathematical and physical sciences. Journal of Homotopy and Related Structures is intended to publish papers on Homotopy in the broad sense and its related areas like Homological and homotopical algebra, K-theory, topology of manifolds, geometric and categorical structures, homology theories, topological groups and algebras, stable homotopy theory, group actions, algebraic varieties, category theory, cobordism theory, controlled topology, noncommutative geometry, motivic cohomology, differential topology, algebraic geometry.