等变拓扑霍奇schild同调中的计算
Computations in Equivariant Topological Hochschild Homology
AI总结：
本文对等变拓扑霍奇schild同调（ETHH）开展基础计算，包括奇素数下ETHH(H𝔽̲ₚ)及等变复配边谱MU_G、MU_ℝ的ETHH计算，为后续相关研究提供输入。
AI中文摘要：
代数K理论中最有效的计算方法之一是迹方法，它将代数K理论与拓扑霍奇schild同调（THH）、拓扑循环同调（TC）进行比较。近期，本文两位作者与Gerhardt共同构造了拓扑霍奇schild同调的等变版本——等变拓扑霍奇schild同调（ETHH），该结构接收来自Merling的真正等变代数K理论的迹映射。本文对ETHH开展基础计算，可为后续ETHH与等变拓扑循环同调的计算提供输入：即对奇素数p，计算ETHH(H𝔽̲ₚ)，展示该场景下Bökstedt周期性的复杂性；还对等变复配边谱MU_G与MU_ℝ计算了ETHH。
英文摘要：
One of the most effective approaches to computations in algebraic $K$-theory is trace methods, which compare algebraic $K$-theory with topological Hochschild homology and topological cyclic homology. In recent work, two of the authors, together with Gerhardt, construct an equivariant refinement of topological Hochschild homology ($\mathrm{ETHH}$) which receives a trace map from Merling's genuine equivariant algebraic $K$-theory. In this paper, we perform foundational computations of $\mathrm{ETHH}$ that can serve as input for future computations of $\mathrm{ETHH}$ and equivariant topological cyclic homology. Namely, we compute $\mathrm{ETHH}(H\underline{\mathbb{F}}_p)$ for odd primes, showcasing the complexity of Bökstedt periodicity in this setting. Furthermore, we give computations of $\mathrm{ETHH}$ for the equivariant complex cobordism spectra $MU_G$ and $MU_{\mathbb{R}}$.
