On realizations of the subalgebra ?^{ℝ}(1) of the ℝ-motivic Steenrod algebra
On realizations of the subalgebra ?^{ℝ}(1) of the ℝ-motivic Steenrod algebra
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关于∄-动机 Steenrod 代数的子代数 ?^{∄}(1) 的实现
DOI：
10.1090/btran/114
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发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Li, A.
中科院分区：
文献类型：
--
作者：
Bhattacharya, P.;Guillou, B.;Li, A.
本文证明了-movic Steenrod代数的和生成的有限子代数可给出128个不同模结构。我们还证明了所有这些模都可以被实现为a-局部有限动机谱的上同调。实现结果是利用Toda实现定理的一个-Motivic类比得到的。我们注意到，每一次实现都可以表示为一个动机自我映射的共纤维。然后，由于Betti实现函子的存在，上述结果的等变类比如下。我们证明了a-等变空间上的分次Steenrod运算与其下空间及其不动点上的经典Steenrod运算之间的关系。然后，该技术被用来识别-等变实现的几何不动点谱。我们发现了-Motivic Toda实现定理的另一个应用：我们产生了Bhattacharya-Egger谱的一个-Motivic，从而产生了一个-等变的类似物，这可能是独立感兴趣的。参考文献
In this paper, we show that the finite subalgebra, generated byand, of the-motivic Steenrod algebracan be given 128 different-module structures. We also show that all of these-modules can be realized as the cohomology of a-local finite-motivic spectrum. The realization results are obtained using an-motivic analogue of the Toda realization theorem. We notice that each realization ofcan be expressed as a cofiber of an-motivic-self-map. The-equivariant analogue of the above results then follows because of the Betti realization functor. We identify a relationship between the-graded Steenrod operations on a-equivariant space and the classical Steenrod operations on both its underlying space and its fixed-points. This technique is then used to identify the geometric fixed-point spectra of the-equivariant realizations of. We find another application of the-motivic Toda realization theorem: we produce an-motivic, and consequently a-equivariant, analogue of the Bhattacharya-Egger spectrum, which could be of independent interest. References