Abstract:
The talk is based on a series of common works with Dimitrii Tyurin and with Denis Osipov.
We prove a version of the famous Goodwillie's theorem with algebraic K-groups being replaced by Milnor K-groups. Namely, given a commutative ring R with a nilpotent ideal I, IN=0, such that the quotient R/I splits, we study relative Milnor K-groups KMn+1(R,I), n⩾0. Provided that the ring R has enough invertible elements in a sense, these groups are related to the quotient of the module of relative differential forms ΩnR,I/dΩn−1R,I. This holds in two different cases: when N! is invertible in R and when R is a complete p-adic ring with a lift of Frobenius. However, the approaches and constructions are different in these cases.