Relative cyclotomic structures and equivariant complex cobordism

Autor:	Blumberg, Andrew J., Mandell, Michael A., Yuan, Allen
Rok vydání:	2023
Předmět:	Mathematics - Algebraic Topology Mathematics - K-Theory and Homology Primary 19D10 Secondary 55P60
Druh dokumentu:	Working Paper
Popis:	We describe a structure on a commutative ring (pre)cyclotomic spectrum $R$ that gives rise to a (pre)cyclotomic structure on topological Hochschild homology ($THH$) relative to its underlying commutative ring spectrum. This lets us construct $TC$ relative to $R$, denoted $TC^{R}$, and we prove some descent results relating $TC^{R}$ and $TC$. We explore several examples of this structure on familiar $\mathbb{T}$-equivariant commutative ring spectra including the periodic $\mathbb{T}$-equivariant complex cobordism spectrum $MUP_{\mathbb{T}}$ and a new (connective) equivariant version of the complex cobordism spectrum $MU$. Comment: This is a preliminary version that depends on the work in progress [Cyc23]
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2310.02348 Zobrazit plný text záznamu View this record from Arxiv