Algebraic theories of power operations

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Topology Pub Date : 2023-12-05 DOI:10.1112/topo.12318

William Balderrama

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引用次数: 2

Abstract

We develop and exposit some general algebra useful for working with certain algebraic structures that arise in stable homotopy theory, such as those encoding well-behaved theories of power operations for $E_{\infty}$ ring spectra. In particular, we consider Quillen cohomology in the context of algebras over algebraic theories, plethories, and Koszul resolutions for algebras over additive theories. By combining this general algebra with obstruction-theoretic machinery, we obtain tools for computing with $E_{\infty}$ algebras over $F_{p}$ and over Lubin–Tate spectra. As an application, we demonstrate the existence of $E_{\infty}$ periodic complex orientations at heights $h ⩽ 2$ .

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幂运算的代数理论

我们开发并展示了一些一般代数，用于处理稳定同伦理论中出现的某些代数结构，例如编码E∞$\mathbb {E}_\infty$环谱的幂运算的良好理论。特别地，我们考虑了代数在代数理论上的Quillen上同调，完备论，以及代数在加性理论上的Koszul决议。通过将这种一般代数与阻碍理论机制相结合，我们获得了F p $\mathbb {F}_p$和Lubin-Tate谱上的E∞$\mathbb {E}_\infty$代数的计算工具。作为应用，我们证明了在高度h≥2 $h\leqslant 2$处E∞$\mathbb {E}_\infty$周期复取向的存在性。

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

Journal of Topology 数学-数学

CiteScore

2.00

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Topology publishes papers of high quality and significance in topology, geometry and adjacent areas of mathematics. Interesting, important and often unexpected links connect topology and geometry with many other parts of mathematics, and the editors welcome submissions on exciting new advances concerning such links, as well as those in the core subject areas of the journal. The Journal of Topology was founded in 2008. It is published quarterly with articles published individually online prior to appearing in a printed issue.