We will introduce the Witt vectors of a ring with coefficients in a bimodule and use them to calculate the components of the Hill-Hopkins-Ravenel norm for cyclic p-groups. This algebraic construction generalizes Hesselholt's Witt vectors for non-commutative rings and Kaledin's polynomial Witt vectors over perfect fields. We will discuss applications to the characteristic polynomial over non-commutative rings and to the Dieudonné determinant. This is all joint work with Krause, Nikolaus and Patchkoria.
- Topology Seminar