Peter Scholze: On topological cyclic homology

The lecture was held within the framework of the Hausdorff Trimester Program : Workshop "K-theory in algebraic geometry and number theory"

Abstract:
Topological cyclic homology is an approximation to algebraic K-theory that has been very useful for computations in algebraic K-theory. Recently, it has also inspired some work in integral p-adic Hodge theory. Its definition however requires delicate tools from genuine stable homotopy theory, and explicit point-set models. In joint work with Thomas Nikolaus, we revisit this theory, by giving a simplified definition of the ∞-category of cyclotomic spectra, and corresponding simplified formulas for topological cyclic homology.