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Relative cyclotomic structures and equivariant complex cobordism
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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 $MU$.
Forward citations
Cited by 3 Pith papers
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Noncommutative Cartier Formulae
A noncommutative Cartier formula for E1-ring spectra is proven and applied to show that p-curvature of the quantum connection computes quantum Steenrod operations for Calabi-Yau symplectic manifolds.
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An algebraic model for rational ultracommutative rings
Geometric fixed points and norms assemble into an equivalence between rational ultracommutative rings and functors on the span category of finite connected groupoids with full backwards and faithful forwards maps.
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An algebraic model for rational ultracommutative rings
Geometric norms together with inflations assemble into a functor that is an equivalence between rational ultracommutative ring spectra and certain functors on the span category of finite connected groupoids.
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