Speaker: Jonas McCandless
Title: Curves on K-theory revisited
Abstract: The spectrum of curves on K-theory was introduced by Bloch in his work on the relationship between K-theory and the de Rham—Witt complex. Bloch’s program was studied further by Hesselholt who established an equivalence between p-typical TR and the spectrum of p-typical curves on K-theory for p-power torsion algebras, and further used this to show that the homotopy of the spectrum of p-typical curves on K-theory is isomorphic to the de Rham—Witt complex for smooth algebras over a perfect field of characteristic p. In this talk, I will present a construction of integral TR which does not rely on equivariant stable homotopy theory similar in spirit to the recent construction of topological cyclic homology given by Nikolaus and Scholze. As an application, we give a formula for TR in terms of the spectrum of curves on K-theory for a connective ring spectrum extending the work of Hesselholt.