G-Theory of F_1-Algebras I: the Equivariant Nishida Problem
G-Theory of F_1-Algebras I: the Equivariant Nishida Problem
复制标题
F_1-代数的G理论I：等变西田问题
DOI：
--
复制
发表时间：
2011
期刊：
影响因子：
--
通讯作者：
Snigdhayan Mahanta
中科院分区：
文献类型：
--
作者：
Snigdhayan Mahanta
我们发展了F_1-代数的一个G-理论，并建立了它的第一性质。我们构造了一个Cartan装配映射，将有限点群的Chu-Morava K-理论与我们的G-理论进行了比较。利用某些分类空间的稳定同伦计算有限点群的G-理论群。我们还构造组合格雷森操作。我们讨论了我们的形式如何与等变西田问题相关--它询问S^G上是否存在赋予oplus_npi_{2n}（S^G）预λ-环结构的运算，其中G是有限群，S^G是等变球谱的G-不动点谱。
We develop a version of G-theory for F_1-algebras and establish its first properties. We construct a Cartan assembly map to compare the Chu-Morava K-theory for finite pointed groups with our G-theory. We compute the G-theory groups for finite pointed groups in terms of stable homotopy of some classifying spaces. We also construct combinatorial Grayson operations on them. We discuss how our formalism is relevant to the Equivariant Nishida Problem - it asks whether there are operations on S^G that endow oplus_npi_{2n}(S^G) with a pre-lambda-ring structure, where G is a finite group and S^G is the G-fixed point spectrum of the equivariant sphere spectrum.