Bass' NK-groups and arithmetic invariants

Abstract: In the 1970s Quillen proved that algebraic K-theory is homotopy invariant for a regular noetherian base. For a non-regular base ring this is not true. Bass defined the NK-groups in order to study the failure of homotopy invariance in K-theory. In general these groups are not well understood, though they have many interesting properties. Ten years ago, Cortiñas, Haesemeyer, Walker and Weibel used cdh-descent methods to understand the NK-groups when the input is rational. In this talk I will explain parts of their work and discuss ongoing work with Elden Elmanto where we aim to extend their methods to the mixed characteristic setting.

algebraic topology

Audience: researchers in the topic

MIT topology seminar

Series comments: We meet at varying times on Monday. Click here to join the zoom meeting . The Zoom meeting room number is 132-540-375.

The mailing list for this seminar is the MIT topology google group. Email Mike Hopkins if you want to join the list.