$C_{p^n}$-坦巴拉场的分类

Noah Wisdom
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引用次数: 0

摘要

坦巴拉函子在等变同构理论中是作为相干交换等变环谱的同构群的固有结构而出现的。我们证明,如果 $k$ 是一个类场$C_{p^n}$-坦巴拉函子,那么$k$ 是一个类场$C_{p^s}$-坦巴拉函子$\ell$ 的联立,从而$\ell(C_{p^s}/e)$ 是一个场。如果这个域的特征不是$p$,我们就会发现$\ell$一定是一个定点坦巴拉函子;如果这个域的特征是$p$,我们就会通过对弗罗贝纽斯内态行为的分析和阿尔丁-施莱尔理论的应用来确定$\ell$的所有可能形式。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A classification of $C_{p^n}$-Tambara fields
Tambara functors arise in equivariant homotopy theory as the structure adherent to the homotopy groups of a coherently commutative equivariant ring spectrum. We show that if $k$ is a field-like $C_{p^n}$-Tambara functor, then $k$ is the coinduction of a field-like $C_{p^s}$-Tambara functor $\ell$ such that $\ell(C_{p^s}/e)$ is a field. If this field has characteristic other than $p$, we observe that $\ell$ must be a fixed-point Tambara functor, and if the characteristic is $p$, we determine all possible forms of $\ell$ through an analysis of the behavior of the Frobenius endomorphism and an application of Artin-Schreier theory.
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