Motivic cohomology reimagined

Abstract: Beilinson, Macpherson and Schechtman asked us to imagine a world where topological K-theory was first defined before singular cohomology. How would one invent the latter? This question has been influential to various approaches to motivic cohomology of smooth varieties with its relationship to K-theory, serving a 'design principle.' I will explain an extension of this idea to define a version of motivic cohomology of singular schemes. The engine behind it is the Bhatt-Morrow-Scholze prismatic sheaves.

This is all joint work with Tom Bachmann and Matthew Morrow.

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.