Relative cyclotomic structures and equivariant complex cobordism

Abstract

We describe a structure on a commutative ring (pre)cyclotomic spectrum that gives rise to a (pre)cyclotomic structure on topological Hochschild homology () relative to its underlying commutative ring spectrum. This lets us construct relative to , denoted , and we prove some descent results relating and . We explore several examples of this structure on familiar ‐equivariant commutative ring spectra including the periodic ‐equivariant complex cobordism spectrum and a new (connective) equivariant version of the complex cobordism spectrum .