Cyclotomic spectra

The fundamental work of Dundas–Goodwillie–McCarthy relates the algebraic K-theory of a connective ring spectrum R to its topologi cal cyclic homology TC(R), which is in turn a functor of the cyclotomic spectrum THH(R). 

In this talk, the speaker will introduce a modern definition of the cate gory of cyclotomic spectra, due to Nikolaus and Scholze. A basic example is given by THH(R) when R is a ring spectrum. The speaker will introduce several invariants of cyclotomic spectra, namely TP, TC−, TC, and TR. They will also briefly mention THH with coefficients in a bimodule, and the related formalism of p-polygonic spectra. Finally, they will give the statement of the Dundas–Goodwillie–McCarthy theorem.

Suggested references: [NS18], [DGM13], [KMN23]